Endogenous assembly rules, senior agenda power,
and incumbency advantage∗
Jon X. Eguia†
Univ. Bristol and New York U.
Kenneth Shepsle‡
Harvard University
October 6, 2013
Abstract
We study repeated legislative bargaining in an assembly that chooses its bargaining rules endogenously, and whose members face an election after each legislative term. An agenda protocol or bargaining rule assigns to each legislator a
probability of being recognized to make a policy proposal in the assembly. We predict that the agenda protocol chosen in equilibrium disproportionately favors more
senior legislators, granting them greater opportunities to make policy proposals,
and it generates an incumbency advantage to all legislators.
Keywords: Seniority, incumbency advantage, endogenous agenda, recognition
rule, legislative bargaining, bargaining rules.
Word Count: 8308.
∗
We are very grateful to Abhinay Muthoo for his contribution as he collaborated with us in the early
stages of this project, to Andrew Hall for excellent research assistance, and to Tasos Kalandrakis, John
Matsusaka, Salvatore Nunnari, Santiago Oliveros, Carlo Prato, John Patty, Razvan Vlaicu and audiences
at USC, Rochester, Wash. U. and Columbia for their comments.
†
[email protected] 19 West 4th St. 2nd fl. Dept. of Politics, NYU. New York, NY 10012, US.
‡
[email protected] 1737 Cambridge St. CGIS-Knafel Bldg. Harvard University. Cambridge,
MA 02138.
1
1
Introduction
Legislative rules affect legislative outcomes. But where do these rules come from? Legislators bargain over them. Then, once procedural protocols are in place, legislators bargain
over policy. The chosen procedural rules have important consequences on bargained policy outcomes, and hence on economic outcomes and welfare. We wish to understand how
rules are chosen, and what effect they have on policy and economic outcomes.
The literature on legislative bargaining (Baron and Ferejohn 1989; Baron 1996; Morelli
1999; Banks and Duggan 2000; Kalandrakis 2004; Penn 2009) assumes that bargaining
occurs under fixed rules.1 But this isn’t always so — rules are often chosen by the bargainers themselves before their actual policy bargaining begins.2 We, along with Diermeier,
Prato, and Vlaicu (2013), advance this bargaining literature by endogenizing bargaining
rules.
A key insight follows from the fact that incumbent legislators want to be reelected. So
they choose rules that help them secure this objective. The rules that help incumbents
get reelected are seniority rules. We identify the rule that helps them the most. This is
a rule that grants disproportionate proposal power to senior legislators, allowing them
to obtain more favorable policies and a greater share of resources for their constituency
(Knight 2005), which induces voters in every district to prefer to reelect their incumbent
better than to elect a newly minted legislator (Levitt and Snyder 1997). The advantages
in the allocation of funds enjoyed by districts represented by senior members distort both
efficiency and equity across regions — it redistributes away from some districts and toward
others creating inequalities unrelated to need or efficiency.
As an empirical matter, seniority is a characteristic feature of many legislative institutions. Senior legislators typically take leadership roles, wield disproportionate clout in
the selection of rules of procedure, and are also influential in determining the proposals
1
Recent work on dynamic legislative bargaining by Dziuda and Loeper (2012); Nunnari (2012); Bowen,
Chen and Eraslan (2012); Nunnari and Zapal (2013); Anesi and Siedmann (2013) and several others
continues to assume that bargaining rules are exogenous, and fixed.
2
A legislative assembly, for example, may be regarded as a self-governing group. Thus the U.S.
Constitution asserts that “each House may determine the Rules of its Proceedings” (Article I, Section
5) and constrains this rule making in only minimal ways.
2
that ultimately come to a vote before the assembly. The modern empirical literature
on the U.S. Congress, beginning with Abram and Cooper (1968) and Polsby, Gallagher,
and Rundquist (1969), insist on the importance of seniority as an organizational principle for the conduct of legislative business. In seeking to explain the legislative reliance
on seniority, however, this literature emphasizes functionalist collective purposes — for
example, the elevation of experienced legislator types to positions of authority — without
giving due consideration to the career or policy goals of individual legislators.3 It fails,
that is, to tell us why it is in the interest of members of a self-governing group to select
procedures that bestow differential advantage on senior members.
In the more analytical literature on legislative organization, McKelvey and Riezman
(1992) were the first to tackle this issue formally (although a more informal development
anticipating theirs is found in Holcombe 1989). They provide an explanation of the
adoption of an exogenously given seniority institution based on the benefit it provides
each incumbent legislator in his or her pursuit of reelection. A seniority rule, in effect,
begets an incumbency advantage. Self-interested legislators, caring only about policies
that benefit their constituencies and thus that enhance their prospects of reelection,
support some form of seniority.
McKelvey and Riezman (1992) consider an exogenously given seniority rule that lumps
legislators in two categories: any legislator reelected at least once is senior, newly elected
legislators are not, and seniors are assigned greater agenda power than the newly elected.
They show that legislators prefer this exogenous binary rule to a default rule that treats
all legislators equally.
We depart from their model by considering the endogenous selection of agenda rules.
We do not restrict the choice to a binary one between a seniority-based agenda rule
and random recognition. Instead, seniority-based rules emerge from an unconstrained
menu of agenda procedures. We not only show that a seniority rule is preferred to an
equal treatment rule; rather, we identify the rule that is selected in equilibrium when
any other rule (and not only the equal treatment default) is available. The equilibrium
3
For exceptions to functionalist arguments, see the Epstein, Brady, Kawato, and O’Halloran (1997).
3
rule is a seniority rule, but it is not the exogenous seniority rule studied by McKelvey
and Riezman, underscoring the limitations of their approach.
In addition, we relax some restrictive assumptions on the use of information by voters
imposed by McKelvey and Riezman; and we endogenize assembly membership by allowing
for both exogenous and endogenous turnover. We discuss these and other advances over
McKelvey and Riezman’s theory in section 6. We highlight that the shadow of a future
election looms large in the incumbents’ choice of legislative rules. Our analysis of electoral
incentives and how they affect the selection of agenda rules is an important difference
between our theory and the work by Diermeier, Prato, and Vlaicu (2013), who study the
selection of agenda rules in a closed assembly with no reelection.
We study a game with infinitely many periods, in which each period possesses two
legislative bargaining stages — a rules-selection stage and a policy-determination stage—
followed by an electoral stage in which voters choose whether to reelect the incumbent
that represents their constituency. The first legislative stage (rules-selection stage), occurring in a “procedural state of nature” (Cox, 2006), determines the bargaining rules in
operation at the policy-determination stage. A legislator is selected to propose a procedural rule as a take-it-or-leave-it proposal that is put to a vote in the assembly. This rule
describes the distribution of proposal power among legislators in the form of probabilities
of recognition to make the first proposal at the policy-determination stage. If this procedural rule is rejected, an exogenous reversion procedure is imposed (equal proposal power
for each legislator). The second stage (policy-determination stage), operating under the
procedures just determined, is the place where actual policy decisions are made.
We let the set of feasible procedural rules include any distribution of proposal power
that conditions each legislator’s proposal power on the legislator’s district, and on her
ordinal seniority. Our theory, therefore, allows procedural rules that treat each legislator differently, unlike previous theories that lump them in two categories. Furthermore,
we allow procedural rules to discriminate among legislators based on factors other than
seniority (see section 5). In our theory, the procedural rule and its characteristics are
endogenously determined: the rule is strategically proposed by a legislator, and strate4
gically voted on by all legislators. We show that equilibrium rules discriminate on the
basis of seniority, not on other factors, and favor more senior legislators. As a result,
the expected payoff to each district is increasing in the seniority of the legislator who
represents it. These procedural rules that favor senior legislators generate an incumbency
advantage. Because a reelected incumbent would always be more senior than a newly
elected challenger, if the assembly operates under procedural rules that favor seniority,
constituents have an incentive to reelect their incumbents, even junior incumbents. By
“incumbency advantage” we mean the difference in the expected utility for a constituency
that reelects its incumbent, minus the expected utility for a constituency that replaces
its incumbent. It is therefore measure of magnitude of the incentive to reelect incumbents created by the strategic selection of legislative bargaining rules. In equilibrium,
incumbents choose such seniority rules to maximize this incumbency advantage.
We emphasize that seniority is unique, in that it is the only attribute that no challenger can ever possibly match. So rules based on seniority create an electoral advantage
that necessarily favors all incumbents.
In the next section we provide the theoretical context. In section 3 we derive some
existence results. In section 4 we deal with the multiplicity of equilibria by proposing and
using a selection criterion: we find the equilibrium that maximizes incumbency advantage, that is, the equilibrium that maximizes the electoral incentive to reelect incumbents.
Our main result is to identify this equilibrium. In section 5 we consider generalizations
and extensions to our theory. Additional comparisons to existing literature and concluding remarks follow in section 6. All proofs of results are relegated to a Supporting
Information section, available online.
2
The Model
Consider an infinite horizon dynamic game Γ played by a fixed set N of voters, one voter
per district, and a set of politicians that represent voters in a legislative assembly.4 Let
4
We initially consider politicians drawn from an infinite pool of homogeneous agents. We introduce
heterogenous politicians with idiosyncratic traits in Section 5.
5
n denote the number of districts and assume n is odd. An arbitrary period is denoted
by t. Let Γt be the period game played in period t. This period game is played by 2n
agents: the n voters and n politicians, each politician serving as the representative of
a given district in period t. Representatives in any given period are strictly ordered by
their seniority in the assembly, measured by the time since they first joined the assembly:
let θt = (θ1t , ..., θnt ) be a state variable that denotes the position of the representative from
district i in the seniority order in period t, where θit = k ∈ {1, 2, ..., n} means that the
representative from district i is the k − th most senior representative in period t.
The period t game Γt has one non-strategic pre-stage, and 3 stages, which we now
describe.
0. Pre-stage: Assignment of seniority order
At the beginning of each period t > 1, we assign seniority ranks θt as follows.5 Representatives who had first joined the assembly in any period t0 < t and serve again in
period t, preserve their relative position from period t − 1, i.e. for any pair of reelected
representatives serving districts i and j, θit < θjt ⇔ θit−1 < θjt−1 . Each reelected repre-
sentative j improves as many positions in the seniority order as the number of positions
vacated by representatives with a more senior position than j in period t − 1 who do not
serve in the assembly in period t. Any new politician who joins the assembly for the first
time in period t receives the last position (n) in the seniority order; if there are k ≥ 2
newly elected representatives, some exogenous (possibly random) rule assigns the k last
positions in the seniority ranking among them.6
1. Rules-selection stage
This stage contains three substages. We refer to them as “rounds.” In the first round,
Nature randomly selects a district. For expositional simplicity, assume that each district
5
Representatives in t = 1 and their seniority ranking are given by an exogenous constitutional process
that precedes the rest of the game.
6
This describes how real legislatures, such as the US House of Representatives, operate. Some measure
of previous service weakly orders all legislators; ties are then broken by the application of second-order
criteria (for example, prior service in one in a hierarchy of offices is used in the U.S. House, e.g., governor,
state senator, state representative, etc); if these should fail to break all ties, randomization is employed
(Kellermann and Shepsle, 2009).
6
is selected with equal probability.7 Let r(t) be the district selected to propose a rule. In
the second round, the representative from district r(t) proposes an institutional arrangement at , in effect a recognition rule indicating the probability that each representative is
recognized to make a proposal in the first round of the policy-determination stage (see
n
X
8
below). Formally, at : N −→ [0, 1] is a function such that
at (i) = 1, which maps
i=1
each district i to a probability, so that at (i) denotes the probability that the representa-
tive from district i is recognized to make the first proposal at the policy-determination
stage. In the third round, each representative votes either in favor of recognition rule at ,
or against it. If a simple majority of representatives votes in favor, the outcome of this
stage is recognition rule at .9 Otherwise, the outcome is the reversion rule at = ā which
recognizes each representative with equal probability in the policy-determination stage;
ā(i) =
1
n
for each i ∈ N. That is, the legislature operates under “general parliamentary
law” in which legislators are treated equally.
2. Policy-determination stage
At this stage, representatives play the Baron-Ferejohn (1989) legislative bargaining
game in which a unit of wealth is divided. This stage has infinitely many rounds. For
each district i, the probability that the representative from i is recognized to make a
policy proposal in the first round ρ = 1 of bargaining is at (i); the probability that
the representative from i is recognized to make a policy proposal in round ρ > 1 (if
bargaining reaches round ρ) is
1
n
for any i ∈ N. That is, we assume that the recognition
rule approved at the rules-selection stage can provide only a transitory advantage to
some representatives in the policy-determination stage, an advantage lasting for only one
round of bargaining. If that first round leads to failure, we assume all representatives are
recognized to make policy proposals with equal probability in any subsequent round.10
A policy proposal is a partition of the unit of wealth among the n districts. Observing
7
We relax this assumption and prove the results with a more general probability distribution in the
Supporting Information section.
8
On the concept of proposal rights as a measure of political power in a democratic assembly, see
Kalandrakis (2006).
9
Our results extend to supermajority acceptance rules as we show in section 5.
10
In section 5 we extend the analysis to multi-round rules-recognition procedures that do not impose
equal recognition probabilities after a failure to determine policy in the first round.
7
the proposal, representatives vote it up or down by simple majority rule. If a proposal
is accepted in round ρ, the stage ends. If not, the stage moves to round ρ + 1 with
probability π ∈ (0, 1), and with complementary probability 1 − π, the stage ends in
bargaining failure, which results in an allocation of zero to each district.11
We allow for, but do not require, exogenous turnover (attrition) among representatives. We assume that at the end of stage 2, with exogenous probability α ∈ [0, 1],
one randomly chosen representative ends her legislative career and exits the game due
to exogenous reasons (e.g., death, elevation to high executive office, selection for a remunerative private-sector position, criminal conviction). Each representative thus faces
probability
α
n
of exogenous exit. If a representative exits the game, the vacancy is filled
and the departing incumbent is replaced with a provisional representative drawn from
the infinite pool of identical politicians.12
3. Election stage
At the last stage of each period, all n representatives still in the game, i.e., those who
do not depart for exogenous reasons, enter an election to retain office. In each district, the
voter in the district chooses whether to reelect her representative or to elect a challenger
drawn from the pool of politicians. If the voter chooses the new politician, he or she
enters the assembly at the lowest level of seniority. Legislators who lose the election exit
the game.
At the end of the election stage, the period ends, each representative (reelected or
not) who took part in the period’s legislative bargaining keeps a fraction λ of the prize
obtained by her district, and the voter in the district obtains a fraction 1 − λ. The game
advances to the next period, with discount δ ∈ (0, 1), so that a stage-payoff of x at period
t + k evaluated at period t has a present value of δ k x.
The game Γ consists of the infinite sequence of period games Γt . We assume that all
agents maximize the present value of their expected stream of period payoffs.
11
This is analogous to assuming that there is discounting at the rate π per round, so the total prize
for each district is discounted by πρ−1 if the proposal would only be accepted in round ρ.
12
A replacement representative enters the assembly with the lowest seniority ranking, but, if elected
at stage 3, she has higher seniority in period t + 1 than any newly drawn politician who first joins the
assembly in t + 1 after winning the period t stage 3 election.
8
For each period t, let τ ∈ {1, 2, 3} denote a stage within the period, let τ = 0 denote
the pre-stage that sets the seniority order for the period, and let ρ ∈ {1, 2, 3, ...} denote a
round within a stage. A history h(t, τ , ρ) contains all the information about the actions
played by Nature and all agents in all periods through t − 1, in all stages of period t
through stage τ − 1, and in all rounds of stage τ in period t through round ρ − 1. Given
h(t, τ , ρ), let h(t, τ , ρ)|(t,1,1) denote the history of play from (t, 1, 1) to (t, τ , ρ), that is,
the history of play within period t up to stage τ and round ρ. Let H be the set of all
histories.
Let θit (h(t, 1, 1)) be the seniority of the representative from district i in period t, as a
function of the history of play up to the end of period t − 1.
A behavioral strategy sj for an agent j is a sequence of mappings, one for each
information set in which player j can be called upon to make a move. Each of these
mappings is a function from the history of play at this information set to the set of
feasible actions for agent j. The representative of district r(t) chooses a probability
distribution (a recognition rule); all representatives make a binary choice approving or
rejecting this probability distribution; then representatives engage in the standard BaronFerejohn bargaining game according to the proposed recognition rule (if accepted) or the
reversion rule (if rejected); finally voters make a binary choice. All agents, at each
information set, can condition their actions on all the information available in the full
history of play leading to that information set. Let s denote a strategy profile, which
maps history of play to an action at each information node in the game.
We are interested in subgame perfect equilibria of the game Γ that are stationary
as defined by McKelvey and Riezman (1992), so that each period game Γt is solved
independently of the history of play in previous periods. We call this Stationarity I.
That is, we seek equilibria made up of behavioral strategies that describe how to play
each period game conditioning only on information available within the period game.
This information includes the characteristics of the representatives serving in the current
period, including their seniority, and their actions within the period, but it does not
include any details of play in previous periods. Furthermore, we are interested in the
9
equilibrium strategies of the policy-determination game that are stationary in the sense
defined by Baron-Ferejohn; without this additional stationarity, the solution to the game
is indeterminate, as almost any outcome could then be sustained in equilibrium (see
Baron-Ferejohn). We call this Stationarity II.
Definition 1 A strategy profile s satisfies Stationarity I if for any district i, for any
players (politician or voter) j and j 0 from district i, for any period t, stage τ and round
ρ, and for any two histories h(t, τ , ρ) and h0 (t, τ , ρ) such that θt (h(t, 1, 1)) = θt (h0 (t, 1, 1))
and h(t, τ , ρ)|(t,1,1) = h0 (t, τ , ρ)|(t,1,1) , it follows that sj (h(t, τ , ρ)) = sj 0 (h0 (t, τ , ρ)).13
Given any representative j, a strategy sj satisfies Stationarity II if for any period t,
any rounds ρ and ρ0 and any history h(t, τ , max{ρ, ρ0 }), sj (h(t, 2, ρ)) = sj (h(t, 2, ρ0 )).
An equilibrium is stationary if every strategy profile satisfies stationarity I and every
representative’s strategy satisfies stationarity II.
The intuition of Stationarity I is that if two histories lead to the same seniority
ranking at the beginning of the period, then in a stationary strategy an agent does not
dwell on details of play in previous periods to decide how to play in the current period.
Stationarity II is the standard stationarity in Baron-Ferejohn bargaining, adapted to the
notation of our framework. It implies that looking only at the policy bargaining stage in
a given period, given two structurally equivalent subgames (two subgames with identical
continuation extended trees), agents play the same strategies in the two subgames; that
is, if probabilities of recognition do not vary, agents play the same way in the subgame
that starts after round 1 of bargaining, or after round k > 1 of bargaining.
As in most voting games, there exist many implausible equilibria in which all representatives vote in favor of any proposal: since no representative is pivotal in this case,
representatives are indifferent about the votes they cast. In a one-shot game, such equilibria are discarded assuming that agents never play weakly dominated strategies, and
always vote as if they were pivotal. The analogous argument for dynamic games is
13
Because we allow for the identity of a district’s representative to vary over time, stationarity of play
by the representative from district i requires symmetry across politicians from the same district: identical
politicians representing the same district must play identical strategies. Our definition of stationarity I
assumes this symmetry.
10
to refine the set of equilibria by requiring each voter to eliminate any strategy that is
weakly dominated in a given voting stage game considered in isolation while treating
the equilibrium strategies of all players as fixed for all future stages and periods. These
are “stage undominated strategies” (Baron and Kalai 1993). Eliminating strategies that
violate stage weak dominance is equivalent to requiring each agent to vote as if she were
pivotal in every subgame in which she is involved (Duggan and Fey 2006). We use this
equivalence to define the refinement.
Definition 2 An equilibrium strategy profile s satisfies stage weak dominance if for any
period t, any representative j and any history h(t, τ , ρ) such that a (rule or policy) proposal
x is put to a vote, given s representative j votes for x if the continuation value for j of
passing x is strictly greater than the continuation value of not passing x, and votes against
x if the continuation value for j of not passing x is strictly greater than the continuation
value of passing x.
Stage weak dominance merely rules out equilibria in which voters vote against their
strict interest because their votes do not count. Our solution concept is subgame perfect,
stationary, stage weakly undominated Nash equilibrium. We refer to these equilibria
simply as “equilibria.”
3
Multiplicity of Equilibria
Our game features multiple equilibria. In the next section, we select the equilibrium that
is most favorable for representatives who seek to maximize their electoral incumbency
advantage against challengers. First we identify a larger class of equilibria.
In order for all voters to have incentives to reelect their representatives, the equilibrium must be such that being more senior is not detrimental; otherwise districts would
replace their incumbent and elect a new representative with the lowest seniority ranking. It suffices that the probability that the representative from district i is included in
other representatives’ minimal winning rules-selection coalition is weakly increasing in
11
the seniority of the representative from i (holding fixed the relative seniority order of all
other representatives). If so, voters do not want to replace their incumbent with a new
politician who would become the most junior, and least powerful, representative.
Our first result may be stated informally as follows: For any period t and any recognin−1
2
representatives obtain probability of recogni-
n+1
;
2n
and ii) the probability that a representative is
tion rule a∗t such that i) under rule a∗t ,
tion
1
n
and the rules proposer obtains
one of those who obtains positive probability of recognition is non-decreasing in seniority,
there exists an equilibrium in which, in each period t, recognition rule a∗t is approved by
the assembly, and all incumbents running for reelection are reelected. Each representative selects a minimum winning coalition (in such a way that in the aggregate senior
representatives are more likely to be selected) and offers
1
n
coalition partners. Let Ci (θt ) ⊂ N be the coalition of size
recognition probability to her
n+1
2
of districts such that i is
included in Ci (θt ) chosen by the representative from i as a function of the seniority order
θt . Let |{i ∈ N : j ∈ C i (θt )}| be the number of districts that include district j in their
minimum winning coalition.
Proposition 1 For any profile of minimum winning coalitions (C 1 (θt ), ..., C n (θt )) such
that |{i ∈ N : j ∈ C i (θt )}| is non-decreasing in the seniority of the representative from
j, there exists an equilibrium in which, in each period t :
i) The rules proposer r(t) proposes recognition rule a∗t such that a∗t (l) =
l ∈ C r(t) and a∗t (r(t)) =
1
n
for any
n+1
.
2n
ii) Recognition rule a∗t is approved by the assembly, and all incumbents running for
reelection are reelected.
If the comparative static between seniority and proposal power for any district j is
such that, holding constant the relative position of all other districts in the seniority
order, the representative from j becomes more likely to be among those who receive
proposal power as she becomes more senior, and this inequality is strict (j becomes
strictly more likely) at some point in the seniority ranking, then each district has a strict
incentive to reelect its incumbent representative, except the district with the most junior
representative, which is indifferent.
12
Example 1 Suppose there are 3 districts, and there is no exogenous turnover (α = 0).14
There exists an equilibrium consistent with Proposition 1 in which the rules proposer
offers
2
3
policy-proposal probability for herself and
1
3
probability for the most senior among
the other two representatives, and hence the probability of being recognized to be policy
proposer is 49 ,
3
9
and
2
9
respectively for the most senior, second most senior, and junior
representative. In the subsequent policy-determination game, the policy proposer gets
2
3
of the cake and, in expectation, the other two legislators get 16 of the cake (ex post one
¡ ¢
¡ ¢
7
for the most senior
gets 13 the other 0). Expected period payoffs are 49 23 + 59 16 = 18
representative,
6
18
for the second most senior, and
5
18
for the most junior. Everyone is
reelected, the two seniors strictly, the junior just weakly in the sense that the voters of
the district are indifferent between reelecting and replacing.
Other equilibria exist as well, including one in which representatives choose coalition partners randomly and are never reelected, and qualitatively different equilibria in
which voters use more sophisticated reelection strategies, such as the one in the following
example.
Example 2 Suppose there are 3 districts, and there is no exogenous turnover (α = 0).
Suppose voters reelect their representative if: i) she is not the most junior; or (ii) she
is the rules proposer; or (iii) she obtains probability of recognition exactly 1/9; and they
replace her if none of these three conditions hold. So the junior representative, when
not the rules proposer, votes in favor of a rule that grants her exactly 1/9 recognition
probability. This makes her a cheaper coalition partner at the rules-selection stage. Thus,
the sequence of stages plays out as follows:
• If a senior is recognized, she proposes
8
9
recognition probability for herself and
1
9
for the junior. The junior and the rules proposer vote in favor of this rule, and it is
approved.
• If the junior is recognized, she proposes
2
3
recognition probability for herself, and
1
3
for a randomly chosen senior. The chosen senior and the junior vote in favor of this
14
For the purpose of this and all other numerical calculations, we take the limit π −→ 1, that is, the
probability that bargaining ends exogenously before reaching an agreement is vanishingly small.
13
rule, and it is approved.
• In the policy-determination game, the policy proposer proposes
herself and
1
3
2
3
of the cake for
to one of the others.
¡ ¢
¡ ¢
The probability that either senior becomes the policy proposer is 13 89 + 13 16 =
¡ ¢
¡ ¢
¡ 2 ¢ 35 ¡ 1 ¢
for the junior it is 13 23 + 23 19 = 16
+ 54 6 =
. Expected period payoffs are 19
54
54 3
¡
¢
¡
¢
2
1
34
for each senior, and 16
, and everyone is reelected.
+ 38
= 108
54 3
54 6
19
;
54
37
108
Notice that for the junior representative, the probability of recognition and the ex-
pected period payoffs are higher in the sophisticated equilibrium in Example 2 than in
the simpler equilibrium in Example 1.
4
Equilibrium Selection
Equilibria in which voters use sophisticated reelection rules, as in Example 2, raise questions of equilibrium selection, since we do not find equilibria such as these very plausible
in terms of the ability of a constituency either to commit to so exotic a voting strategy
or to communicate this strategy to its representative even if it could commit. We select
equilibria in which voters do not use such sophisticated rules. Instead they use reelection
rules that condition only on the outcome of the policy-determination stage. In particular,
a standard cutoff rule is used according to which a legislator is reelected if and only if
she provides a period payoff at least as high as the cutoff (assumed fixed across periods).
We stress that we require the equilibrium strategies to be robust against any strategies,
including sophisticated ones that condition on all available information about the history
of play.
Cutoff reelection strategies rule out unintuitive equilibria such as the one in Example
2, but they still allow for a variety of equilibria, including both equilibria in which
incumbents get reelected, as in Proposition 1, and those in which legislators serve for
one term, choose rules that do not favor seniority, and are never reelected.
We argue that among all equilibria, representatives have a common incentive to coordinate on those in which they are reelected along the equilibrium path, which maximize
14
their aggregate expected utility. Among all the equilibria that maximize their aggregate expected utility by guaranteeing their reelection, we argue that representatives will
coordinate on one equilibrium in particular: the one that maximizes their incumbency
advantage.
Somewhat casually, by “maximize incumbency advantage” we mean that incumbent
representatives will seek arrangements which, ex ante, maximize the present discounted
value of their payoff minus that of a newly elected politician. Because both constituency
payoffs and representative payoffs are proportional to the share of wealth secured in the
equilibrium outcome (no moral hazard), constituents are provided the sharpest incentives
to prefer their incumbent over a challenger when this difference is maximized. Replacing
their incumbent with a newly minted representative when the incumbency advantage is
maximal imposes the largest cost on the constituency. Incumbency advantage in our
model is a valence that arises endogenously as a result of the institutional rules chosen
in the assembly, and makes the incumbent more attractive than a potential challenger.15
Previous theories of elections with endogenous candidate valence assume that politicians
can engage in costly actions to increase their valence (Ashworth and Bueno de Mesquita
2008, 2010; Serra 2010). We show that incumbent representatives have a unique opportunity to increase their electoral valence at no cost by approving procedural rules that
favor seniority.
More formally, let E denote an equilibrium. Let φi,y
t (E) be the present value of the
expected stream of future payoffs evaluated at the end of period t for a district i that
reelects its incumbent, given that continuation play will be according to equilibrium E.
Let φi,n
t (E) be the same present value if the district does not reelect its incumbent.
i,n
Then the incumbency advantage of legislator i is φi,y
t (E)− φt (E), i.e. the value of
reelecting the incumbent from district i given her seniority minus the value of replacing
15
Valence characteristics are those on which there is a constituency consensus that more is preferred
to less, in contrast to positional characteristics (left-wing versus right-wing issue positions) on which
a constituency may be divided. The literature on the importance of valence in electoral models and
voting behavior is large. A sampling includes Ansolabehere and Snyder (2000), Aragones and Palfrey
(2004), Enelow and Hinich (1982), Groseclose (2001), and Stone and Simas (2010).
15
the incumbent with a challenger. The average incumbency advantage is
n
i,n
X
φi,y
t (E) − φt (E)
i=1
n
X φi,n
1
t (E)
=
−
,
(1 − δ)n i=1
n
n
where δ is the voters’ discount factor across periods.16 The average or aggregate incumP
bency advantage is maximized if ni=1 φi,n
t (E) is minimized.
Let E be any set of equilibria of the game.
Definition 3 We say that equilibrium E ∈ E maximizes incumbency advantage
P
within E if E = arg min ni=1 φi,n
t (E), that is, if E minimizes the average present value
{E∈E}
of the expected stream of payoffs of a district that replaces its incumbent.
One reason to seek to maximize incumbency advantage is to create the greatest possible electoral advantage over any challenger. Consider two minimal extensions to our
model. First, assume that representatives, all else equal, prefer to win each election by
the largest possible margin, that is, they value margin of victory lexicographically, as a
second priority, after their objective of maximizing their share of the pie. Second, relax
the simplification of a single representative voter in each district, and assume that in each
district there is a continuum of voters [−1, 1], and assume that for any voter v ∈ [−1, 1],
voter v has a preference bias of v for the incumbent, so that v in district i votes for the
incumbent if
i,n
φi,y
t (E) − φt (E) + v ≥ 0.
(1)
i,n
Then, any voter v ∈ [max{−1, −(φi,y
t (E) − φt (E))}, 1] votes for the incumbent, and
©
ª
i,n
the incumbent’s margin of victory is min φi,y
t (E) − φt (E), 1 , which all else equal,
i,n
incumbents would like to maximize by maximizing φi,y
t (E) − φt (E).
There is a second intuition that rationalizes the selection of the equilibrium we identify. Imagine (outside the model) that the share of the bargaining outcome that a representative keeps for herself, instead of being exogenously fixed at λ, were endogenously
P
Note that ni=1 φi,y
t (E) is the present value of an infinite stream of the total wealth to be distributed
1
each period (one unit). With discount δ, this value is 1−δ
.
16
16
chosen by the representative. If some institutional rules generate a bigger incumbency adi,n
vantage φi,y
t (E)−φt (E), then the incumbent would be able to appropriate a larger share
of this surplus, instead of passing it on to her constituents, and still be reelected. Maximizing incumbency advantage through procedural arrangements thus facilitates “corruption” (personal venality, directing funds or tax breaks or insider information to friends
and family, etc.) by allowing seniors to extract rents that are a function of the difference
between senior and junior bargaining outcomes. Representatives will want to maximize
this difference.
Incumbency advantage is maximized by making the payoffs to junior representatives
as small as possible in the bargaining game, which maximally punishes any constituency
that replaces its incumbent. In particular, by zeroing out the probability of recognition
of all junior representatives (those with less than median seniority), a constituency that
replaces its incumbent will be required to wait the maximal amount of time, given exogenous turnover, before their newly minted representative rises sufficiently on the seniority
ladder to qualify for positive probability of recognition and a greater than minimal expectation of payments. In sum, an institutional arrangement that maximizes incumbency
advantage is such that the stream of future payoffs for the constituency that replaces its
representative remains very low for as many periods as possible, which is achieved by
concentrating all the probability of recognition on senior representatives.
It could be argued that each incumbent would prefer the equilibrium that maximizes
her own incumbency advantage, rather than the equilibrium that maximizes total or average incumbency advantage, and this could lead to some coordination problems. However, note first that incumbents cannot affect their own incumbency advantage; rather,
by choosing coalition partners at the rules stage, the representative from i can affect the
incumbency advantage of any other representative, but not her own. It is the other representatives who determine i0 s incumbency advantage, by their own choices when they
are the rules proposer. This mutual dependency induces coordination on the mutually
beneficial rule that maximizes aggregate incumbency advantage. Furthermore, the equilibrium that maximizes total or average incumbency advantage is also the equilibrium
17
that maximizes individual incumbency advantage for a majority of incumbents, including
the incumbent with median seniority. We thus find it doubly focal, even if politicians
have no proclivity toward collusion.
A technical quibble on equilibrium selection is in order. At the policy-determination
stage of any period, the remainder of the stage after the first policy proposer is drawn
is identical to the remainder of the Baron-Ferejohn (1989) bargaining game after the
first policy proposer is drawn. An equilibrium is such that the policy proposer forms
a coalition of minimal winning size by offering fraction
1
n
of the cake to exactly
n−1
2
legislators and keeping the rest for herself. Conditional on not being the proposer in
bargaining round ρ, each legislator must be chosen for inclusion in the round ρ coalition
with equal probability. In the standard, symmetric equilibrium of the Baron-Ferejohn
game, the proposer randomizes over her coalition partners.17 We select equilibria in
which, at the policy-determination stage in each period t, equilibrium play follows this
standard, symmetric solution at the policy-determination stage.
Let E 0 be the set of equilibria that satisfy the following properties:
Property 1 Voters use cutoff reelection rules, and incumbents are reelected along the
equilibrium path.
Property 2 For any period t, at the policy-determination stage of period t, representatives play the symmetric solution to the Baron-Ferejohn game.
Within the class of equilibria satisfying these properties, we find the equilibrium that
maximizes the electoral incentives to reelect incumbents.18 This is our main result. Let
N −r(t) = N\{r(t)} denote the set of districts excluding the district of the rules proposer
r(t).
17
Alternatively, in asymmetric equilibria, different proposers choose different coalitions, but in such a
correlated way that ex-ante all agents are equally likely to be included in a coalition (for instance, with
n = 3, agent 1 may always choose agent 2, who always chooses agent 3, who always chooses agent 1; see
Baron and Ferejohn (1989), footnote 16).
18
The set E 0 is not empty, so the equilibrium that maximazes seniority advantage within this set exists.
For instance, the class of equilibria identified in Proposition 1 belongs to E 0 .
18
Figure 1: Margin of victory as a function of number of terms in office.
Proposition 2 If the exogenous probability of attrition α is strictly positive, there is an
equilibrium that uniquely maximizes incumbency advantage in E 0 . In this equilibrium, in
each period t, the rules-recognition rule a∗t assigns probability of recognition a∗t (i) =
to the
n−1
2
a∗t (r(t)) =
1
n
most senior representatives in N −r(t) and leaves the remaining probability
n+1
2n
for the rules proposer. If α = 0, this equilibrium still maximizes incum-
bency advantage, but not uniquely.
Incumbency advantage is maximized by forming a coalition of minimal winning size
with the rules proposer and the most senior representatives, and distributing all the
probability of recognition within this senior coalition. Under the assumption that the
probability to be recognized to make a rules proposal is uniform across all representatives,
the present value of the stream of payoffs for each district in this equilibrium is strictly
increasing in seniority for districts with a representative with less than median seniority,
and constant at the highest value for any representative with at least median seniority.
Assuming a continuum of distinct voters in each district who vote for the incumbent
only if expression (1) holds, an empirical implication is that the margin of victory for
representatives must be strictly increasing in seniority for junior legislators up to those
with median seniority, and then flattening out.
We provide some tentative descriptive evidence that suggests that this prediction is
19
largely consistent with the evidence from the U.S. House of Representatives (Figure 1).
In this figure we plot sixty years of elections to the U.S. House of Representatives (19482008). On the horizontal axis is the number of terms served and on the vertical axis is
the mean incumbent plurality (based on the top two candidates), in percentage points.
Thus, those with one previous term of service averaged a 22% plurality, i.e., a 61% − 39%
victory. Each term-of-service mean plurality is represented by a small circle centered on
a dark line the length of which is proportional to the number of observations in that
category. As displayed, plurality rises with service on average until about the third term
and is flatter thereafter. Since the average median length of service over the sixty year
period is 3.84 terms, the results conform to our theoretical expectation.19
5
Generalizations and Extensions
In this section we introduce four generalizations and extensions; showing that our theory
is robust if we consider supermajority voting rules, if we use instead a cardinal notion of
seniority that classifies legislators in cohorts according to the number of terms they have
served in office, if we allow for rules that specify different probabilities of recognition in
each round of bargaining, or if we account for heterogeneous politicians with idiosyncratic
traits.
We provide a more detailed exposition and a formal statement and proof of each of
our results for these four extensions to the theory in the Supporting Information section.
5.1. Supermajority Voting Rules.
Consider a generalized game in which in any period, q ∈
£ n+1
2
¤
, n − 1 voters are needed
to approve a rules proposal; if a super-majority q in favor of the proposal fails to materialize, the equal recognition rule is used in the subsequent policy-determination stage.
Proposition 2 generalizes, but the supermajority requirement forces the rules proposer
to grant recognition probability to more representatives: the equilibrium that maximizes
19
We thank James Snyder for providing these data. A systematic statistical analysis, arriving at
conclusions similar to ours, is found in Gelman and King (1990). Note that the data for more than 10
terms is noisy because of very small numbers.
20
incumbency advantage is such that, in each period t, the equilibrium recognition rule a∗t
assigns probability of recognition a∗t (i) =
1
n
to each of the q − 1 most senior representa-
tives other than the rules proposer, and leaves the remainder probability 1 −
q−1
n
to the
rules proposer.
5.2. Seniority by Number of Terms.
Consider a game with a cardinal notion of seniority that classifies legislators in cohorts
according to the length of service in office, instead of ordering. The only difference in the
notion of seniority is that the cardinal notion does not break ties among representatives
first elected in the same period. The result is nearly identical: the equilibrium that maximizes incumbency advantage with the cardinal notion of seniority is such that the rules
proposer offers probability of recognition
1
n
to a minimal winning coalition of represen-
tatives, and keeps the rest to herself, and this coalition includes all representatives more
senior than the median, and no representatives less senior than the median (except the
rules proposer herself if she is junior). The only difference is that with seniority cohorts
rather than a strict order, the set of representatives with median seniority need not be a
singleton, and the rules proposer is free to choose any subset of representatives who first
joined the assembly at the same time as the median to complete her minimal winning
coalition.
5.3. Multi-Round Recognition Rules.
The institutional arrangement at that we have considered so far involves the selection
in the period t rules stage of a distribution of recognition probabilities for the first round
of bargaining in that period’s policy-determination stage. If the policy-determination
stage moves on to a second (or subsequent) bargaining round, we have assumed that all
representatives are recognized to make a proposal with equal probability n1 . That is, our
results thus far have assumed an exogenous default distribution of recognition probabilities for each bargaining round beyond the first. Suppose we relax this assumption and
we allow the representative selected as rules proposer to propose a (possibly different)
distribution of recognition probabilities for each possible round of policy bargaining. A
recognition rule then indicates the probability that each representative from district i is
21
recognized to make a proposal in each round of bargaining ρ.
The equilibrium that maximizes incumbency advantage in this game with the richer
set of feasible bargaining rules is such that in each period t, the equilibrium recognition
rule a∗t assigns, in each round ρ, probability of recognition a∗t (ρ, r(t)) =
rules proposer and a∗t (ρ, i) =
1
n
for each of the
n−1
2
n+1
2n
to the
most senior representatives from
districts other than r(t), while all other representatives are assigned zero probability of
recognition. Multi-round recognition rule proposals allow rules proposers to completely
exclude
n−1
2
representatives from any share in the wealth to be distributed, because
they have no agenda power in any round so that their continuation values are zero.
Incumbency advantage is maximized by excluding the most junior representatives. As
a result, representatives who are not the proposer and are less senior than the median
representative obtain a period payoff of zero.
5.4. Heterogeneous Politicians.
We assumed throughout that politicians, except for the district they represent and
their actions in the assembly, are identical. If politicians differed on socio-demographic
traits, one may wonder whether representatives could maximize incumbency advantage
forming minimal winning coalitions based on these socio-demographic traits, instead of
based on seniority. We show that this is not the case: there is something special about
seniority that sets it apart from any other attribute. Even if representatives can collude
to approve bargaining rules that favor some representatives over others based on age,
gender, profession or a myriad of other attributes, only rules based on seniority maximize
incumbency advantage.
The intuition is simple: for any other attribute, a challenger can match the incumbent’s value. If old (or young), female (or male), highly educated (or uneducated) or rich
(or poor) representatives obtain greater proposal power, a constituency that wishes to
replace its incumbent may be able to find a challenger with the favored traits in age, gender, education or wealth, so that the incumbent has no advantage, and can be replaced.
Seniority in the assembly, on the other hand, cannot be matched by any challenger. Seniority is specific to incumbents, and seniority rules thus provide a unique advantage to
22
incumbents. We thus predict that in equilibrium, incumbents choose rules that favor
seniority.
Formally, let X be a finite set of possible socio-demographic trait configurations. Let
xit ∈ X be the socio-demographic trait configuration of the representative from district i in
period t. Let xt = (x1t , x2t , ..., xnt ) be the profile of trait configurations of all representatives
in period t.
Relax our solution concept to let xt be part of the state variable so that stationary
strategies can condition on (xt , θt ) and on all period-t actions. For each district i and period t, let yti be the traits of the politician who contests the election against the district’s
incumbent. We refer to this politician as the challenger. Assume that the challenger
emerges as the winner of an (unmodeled) open primary, so that traits yti are optimal
given the equilibrium, in the sense that they are the traits that maximize the discounted
expected payoffs for the district subject to electing the challenger. In other words, the
challenger has the traits that voters would most like the challenger to have if the challenger had to serve in office (the intuition is that a challenger with worse traits would
be defeated at the primary election). Then, in the general election, the voter chooses
whether to reelect the incumbent with traits xit , or to elect the challenger with traits
yti . The key insight is that if recognition rules depend exclusively on xt and not on θt ,
and yti = xit , then the incumbent from district i has no incumbency advantage over her
challenger.
In consequence, our main seniority result (Proposition 2) is robust to the consideration of heterogeneous politicians: while new equilibria arise that condition on sociodemographic individual traits, the equilibrium in which recognition rules favor senior
representatives is the one that uniquely maximizes incumbency advantage.
6
Discussion
Formal research on the origin of institutional rules that favor seniority in legislatures
begins with the seminal paper by McKelvey and Riezman (1992) —thereafter, MR92.
23
They establish that legislators engaged in Baron and Ferejohn (1989)-style bargaining
games prefer a legislative rule that gives agenda recognition advantage to all legislators
who have been reelected at least once, to one that treats all legislators equally. This
formalizes an informal argument of Holcombe (1989).
The political imperative that drives these organizational choices is an incumbency
advantage. Rather than taking the bargaining game as one in which each legislator has
a fixed likelihood of being recognized to make a proposal, legislators use their control
of the rules to assign recognition likelihoods differentially with the aim of inducing constituencies to reelect their incumbents. They do this by selecting rules that make it
disadvantageous for a constituency to replace its incumbent representative with a newly
minted legislator.
MR92 show that legislators prefer an exogenously given seniority rule over a default
rule that treats all legislators equally in a model in which assembly membership is fixed,
seniority is a binary category, and the strategy sets of all agents are artificially constrained
to limit how agents use their information. In contrast, we let legislators endogenously
choose the alternative rule that (in equilibrium) replaces the equal recognition rule; we
endogenize membership in the assembly; we consider a richer definition of seniority; and
we drop the artificial restrictions on how agents can use information. These theoretical
lead to new and more realistic results.
i) Endogenous versus exogenous rule selection. MR92 allow for only two exogenously
given options at the rules-selection stage: either each legislator is equally likely to be selected to make a policy proposal or only senior legislators share agenda power (equally),
where the definition of “senior” is exogenously given to encompass any incumbents reelected in the previous period. In an extension, Muthoo and Shepsle (2013) allow for an
endogenous definition of who qualifies as senior, but they otherwise maintain the binary
restriction on the menu of options: the alternatives are either equality, or equal privilege for all senior legislators. In our theory, the menu of options is unconstrained: at
the rule-proposal stage of our model, a rules proposer may offer any vector of recognition
probabilities. The rule proposed may favor seniors, or juniors, or specific districts, or other
24
legislator traits. Among all rules, one conditioned on legislator seniority alone emerges
endogenously, but this is an equilibrium feature, not something exogenously imposed.
ii) Endogenous versus exogenous assembly membership. There is no turnover in the
MR92 legislature. A defeated incumbent is simply demoted to the non-senior category.
In our paper constituencies may replace their incumbent (who thus exits the game upon
electoral defeat) and there is always some chance α > 0 an incumbent departs for exogenous reasons. Hence there is churning in assembly membership, a more plausible
condition than one with fixed membership.
iii) Ordinal versus categorical seniority. MR92 and Muthoo and Shepsle (2013) assume that seniority is binary: a legislator either has seniority or does not. However, in
reality (at least in the US Congress), seniority is ordinal: it consists of a strict ranking
or order of legislators from most senior to least senior. We develop our results under an
ordinal notion of seniority.
iv) Use of information. MR92 artificially restrict how agents can use the information
they possess, ruling out as infeasible any voter strategy in which, when deciding how to
vote at the election, the voter takes into account her representative’s actions (i.e. proposals made, or votes cast) in the assembly. As a result the strategies used in MR92’s
equilibria are not shown to be true best responses: it is not established whether a profitable deviation would exist if agents were allowed to use all the information they possess.
In marked contrast, but in line with standard game theory, we allow agents to base their
decisions on all the information at their disposal, which generates new equilibria (Example 2). When in section 4 we select equilibria with simpler stationary strategies, we prove
that these equilibrium strategies are robust against deviations to any other strategy, including non-stationary and arbitrarily sophisticated ones in which agents condition on
the history of play in any way.
v) Identical versus heterogeneous politicians. In Section 5 we introduce idiosyncratic
trait profiles for each politician, we expand the set of feasible legislative rules to allow
those that condition on these traits, and yet we predict that the rule that emerges in
equilibrium continues to be a rule that conditions exclusively on seniority, and not on
25
other traits.
vi) Equilibrium predictions. In MR92’s equilibrium, all legislators share agenda power
equally, and all districts have equal expected payoffs. In contrast, we show that this
arrangement is not an equilibrium if the rules proposal emerges endogenously. In our
equilibrium, positive recognition probability is enjoyed only by the selected rules proposer
and his or her
n−1
2
most senior colleagues.
In short, in a much more general setting, we establish in our first two propositions
that a “seniority equilibrium” exists, one different from that identified by MR92, that the
latter is not an equilibrium, and that among the equilibria that exist in our formulation,
after excluding those that fail to satisfy either stationarity or stage undominance, the
seniority equilibrium we identify uniquely maximizes the incentives of constituents to
reelect incumbent legislators.
This equilibrium does not privilege other characteristics of a legislator or the district
she represents. Suppose, for example, district i were privileged by the rules to make
proposals in the policy-determination stage. While constituents in that district would be
delighted with this advantage, it provides no incentive for them to reelect their representative, since her replacement would inherit this advantage. Her seniority, on the other
hand, would not be inherited by a victorious replacement.
Other research papers identify agenda power and the selection of voting rules as key
aspects of majoritarian decision making in legislative bodies. Early papers by Romer
and Rosenthal (1978), Banks and Gasmi (1987), and Harrington (1990) (along with
the aforementioned Holcombe (1989) and Baron and Ferejohn (1989)) make clear that
agenda power affects equilibrium outcomes, showing that payoffs are skewed toward those
possessing the power to propose. In each of these papers the agenda institutions are taken
as given rather than chosen.
A number of more recent papers provide insights about specific features of agenda
institutions. Breitmoser (2011) considers a variation of the Baron-Ferejohn bargaining
game in which the identity of the policy proposer is deterministic for a finite number of
rounds, and it varies across rounds. Fan, Ali, and Bernheim (2010) examine a dynamic
26
Baron-Ferejohn bargaining setting in which at time t the agents know the subset of agents
who will have positive recognition probability at time t + k. In both of these papers, as
in the earlier papers, the details of the agenda-power arrangement are given exogenously.
Yildirim (2007, 2010) assumes that each legislator’s probability of recognition is proportional to the effort that the legislator invests into gaining agenda power; since becoming
a proposer is costly, he finds that expected payoffs are less unequal. While these papers
show that various agenda institutions can exaggerate or diminish the skew in expected
payoffs, they provide no sense of whether such arrangements would ever have been chosen
by the legislature in a “procedural state of nature.”20
Agenda setting, and the endogeneity of agenda institutions, is central to a recent paper by Diermeier, Prato and Vlaicu (2012). They consider a “procedural state of nature”
in which a self-governing group selects the procedures by which it will conduct its business. They note two stylized facts: (1) Procedures are restrictive, granting asymmetric
agenda advantage to some agents; and (2) Procedures are persistent, that is, not (often)
revoked by a majority. They explain these facts a in one-dimensional model with BaronFerejohn bargaining and single-peaked legislator policy preferences. They account for the
first fact with an appeal to risk aversion — symmetric recognition rules lead to undesirable
policy variance. For the second fact they appeal to opportunity costs — time spent on
revisiting procedural decisions is time taken away from substantive policy making in a
busy legislature. These conceptual developments require additional theoretical machinery (one-dimensional policy space, concave utility functions, costly decision making) that
specializes the argument. While bargaining in a legislative assembly is a possible application of Diermeier, Prato and Vlaicu (2012), their theory is static: it considers only
one session of the assembly, and at the end of this legislative session, the game ends.
Since there is no future and no election, legislators need not take into account reelection
pressures and thus there is no scope to study the incentives to institute seniority rules.21
20
Other contributions focus attention on specific features of agenda-setting rules, such as voting rules
that depend on the motion on the floor (Gersbach 2004); proposal power that is retained across bargaining
periods (Cotton 2010); or reconsideration of an approved policy (Diermeier and Fong 2011).
21
More generally, Duggan and Kalandrakis (2012) establish existence of an equilibrium in a dynamic
model in which committee members choose procedural rules and policy in each period. The set of agents
27
To sum up, we present a dynamic electoral theory of institutions and legislative
bargaining, which advances an understanding of the relationship between procedural
choice and seniority, and their connection to an incumbency advantage. Moving beyond
earlier models in which the procedural options are limited and pre-determined, our model
allows the procedure itself to be endogenously determined. We identify an equilibrium in
which the proposer and senior colleagues share proposal power and juniors are excluded.
We demonstrate that this seniority rule is chosen in equilibrium — it is proposed, passes
the assembly, and produces a subsequent electoral result in which constituencies prefer
to reelect their incumbent representatives. While it is not the only equilibrium rule, it
uniquely maximizes the incentive for a constituency to maintain its representative’s place
on the seniority ladder — the pressure to reelect is at a maximum.
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