LECTURE
2:
POLITICIANS
ELECTORAL
COMPETITION
BETWEEN
OPPORTUNISTIC
Some problems are related to the Pure Majority Rule:
Unrealistic: in reality, the way a society chooses his economic policies is by choosing
politicians. Then, the government chooses the policies. We don’t choose directly which
policy we want. The decision of the politicians will be influenced by what voters want but
it is not direct.
Practical reason: the conditions needed for the rule don’t hold. Indeed, one policy has
many items (q is multidimensional).
Example: the government budget has many items:
- tax rate
- government spending: f1, f2 (two dimensional policy)
In this case, the medium voter could not be applied.
Moreover, the preferences will often not be single peaked or single crossing.
Example:
W
In this case, the individual prefers
extreme policies.
α
β
q
To solve this problem, we will use different tools.
The electoral competition:
Why does someone make politics? Motivation of politicians?
- motivated by what they can do (policy motivated)
Example: green party, communist…
They are convinced that they can do politics in another way that is more consistent with
their ideology.
- for fame, money and power (office motivated)
Do the politicians have to implement the platform once elected? Commitment to platform?
They can have different commitment to the platform they propose. There are two extreme views:
-
Full: once they are elected, they implement what they promised. It is like a contract they
respect.
Full discretion: they don’t commit to their platforms because voters don’t believe the
promises or they are not legally committed to do it.
In reality; there is no legal contract which imposes to apply the policy once elected so full
discretion is used (do not have to commit to the platform announced). However, one
good reason to implement the platform is to be re-elected (not particularly for one
politician but for the party he belongs). Full commitment is legally not true but we will
see we can construct it (thanks to reputation concerns).
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The table below summarizes the different cases and links them to chapters of the course.
Motivation of politicians
Commitment to platform
Full
Full discretion
Office motivated
Policy motivated
Chapter 3
Agency (chapter 4)
Partisans (chapter 5)
Politicians (chapter 5)
The electoral competition with office motivated candidates (no rents):
Let’s assume that:
- We have 2 candidates, A and B, (opportunistic)
- Competing by proposing platforms gA and gB
- “If you vote for me, I’ll implement q” (full commitment to platform)
Model:
y i ~ F (.)
Income distribution ( people doesn’t have the same revenue)
E( yi ) = y
50% of voters are on the left side of the median voter, 50% are on the
y : F ( y ) = 1 / 2 right side.
Is the median voter’s income lower or higher than the income mean?
y m ≤≥ y ?
m
m
f(y)
There are a large number of people with low
income, that’s why there is the redistribution
mechanism in some countries.
ym
mean y
y
Because a lot of people have a small income, the mean is higher than the median.
Preferences of each individual:
wi = ci + H(g) , H’>0>H’’ (concave function)
Quasi-linear preferences depending on
private consumption and on the benefit
from public goods.
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Policies are:
- non targetable taxes τ ∈ [0,1] : same taxes for everybody (in reality, it is not true for very
poor developing countries)
- non targetable public goods (gi=g≥0). Example: a park can be targeted because only
people living close to it will take advantage of it.
Each individual maximises his utility under the budget constraint:
MaxU
i
= C i + H (g)
ci
C = (1 − τ ) y i
i
Remark: public goods are not in the budget constraint because it is directly consumed.
From this budget constraint, we can rewrite the utility we get by maximizing the utility of the
individual i (and we get the policy preference):
^
W = (1-τ)yi + H(g)
Government Budget Constraint:
τy = g
If we take into account the government budget constraint(τ y = g) and we replace it in Ŵ :
^
W = H(g) + (1-g/y)yi
i
^
y
is the ratio of the individual income and the average
y
income. For the median voter, we have a below average income,
hence, yi/y<1.
W = H(g)+(y-g) yi/y
where
^
W (g, yi)
Which kind of preferences is it?
∂ ²W
−1
=
<0
y
∂g∂y i
Single crossing property (involves that the Condorcet winner
exists) is satisfied.
We now try to find the preferred policy for each individual:
i
Max W = H(g)+(y-g) y /y
g
How much the person is happy depends positively on g but
also negatively on it because g must be financed by taxes (that
diminishes consumption). That shows the trade off between
private consumption and public goods (if we increase public
goods, this leads to an increase in taxes that drops the private
consumption).
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First order condition:
y
∂W
= H g (g) − i = 0
∂g
y
Where H g (g) is the marginal benefit (independent of the income) of an
i
y
H g (g) =
y
i
increase in public goods by one unit.
y
is the marginal cost of an increase in
y
public goods by one unit.
If you have an income higher than the average income, you will suffer more if we increase the
amount of public goods because taxes are paid proportionally to your income.
From this condition, we can derive the preferred policy for any income yi :
i
i
y
y
H g (g) =  g = H −g1( )
y
y
Timing of the game (Downsian competition)
1
Candidates
announce
platforms
2
Voters vote
3
Winner
implements
the platform
4
End of the
game
What will be the announcement for the candidates A and B (the equilibrium platform)?
Assumption: the candidates are office motivated.
Both of them will announce the preferred policy of the median voter. Here, they will do anything
to win and don’t care about policy at all.
The candidate A must maximise his probability of winning the elections and B does the same:
Max pA.R
Max pB.R
gA
gB
Example:
Candidates announce:
gA= gm+x
gB = gm + x – ε (to be closer to the median voter. If B does that, he wins the election with 100%
probability). Like this, B gets all the rich voters and the median voter and someone else.
Candidate B
Candidate A < 50%
gm gm+x-ε gm+x
=gA
=gB
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This is not an equilibrium because there is always an incentive to reduce g. Both g will converge
and gA = gB = gm
In conclusion, there are 2 predictions:
-
The platforms proposed will be identical
Both candidates will propose gm
pA = probability for A to win the elections:
0 if Wm(gA) < Wm(gB)
pA
½ if Wm(gA) = Wm(gB)
1 if Wm(gA) > Wm(gB)
As soon as you deviate from case ½, you loose the elections with probability 100% (= Bertrand
competition where firms are competing by setting prices: the new firms undercut the others and
attract all the demand - until the price is equal to the marginal cost).
In this model, candidates compete aggressively because of one reason: the fact that voters care
about their utility. In reality, there are also ideological concerns. A and B are not homogenous,
they care about ideology.
Probabilistic voting:
Voters care about characteristics of the policy makers (reputation of the party, …). This model is
a more realistic one.
g
g
m
g
B
A
g =g
B
Before party B undercut party A, voters were indifferent between A and B. Now that B is closer
to the median voter, the party B gets all the voters located on the left of gB.
Let’s assume we have three groups of voters in the group J:
- poor (P)
J
- middle income (M)
- rich (R)
Such that: yR > yM > yP
Since they have different levels of income, they have different policy preferences:
gR < gM < gP the rich ones prefer to have less public goods (g) because they will finance a
bigger part of it.
One individual voter i in group J prefers A to B if the utility he gets in group J under policy A is
bigger than the utility he gets in group J under policy B + some ideological characteristics + δ.
WJ(gA) > WJ(gB) + σiJ+ δ
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σiJ for a certain voter > 0 interpretation: A has to give me a higher utility than B plus a certain
margin of utility to vote for A. There must be a significant gap between A and B for me to vote
for A. Indeed, in this case, voter i has an ideological bias towards B and A has to over compete B
by a positive number.
σiJ is the measure of the ideological bias (which is different for every voter). Inside J, the same
share of voters is biased in favour of A and B.
 1
1 
σ iJ ~ − J , J 
 2φ 2φ 
σiJ
-
0
=
neutral
1
2φ
J
Biased towards A
1
2φ J
Biased towards B
Some voters in J have a positive or a negative σiJ , the ideological preferences cancel each other.
Suppose I’m managing to outperform my rival: to attract ALL the voters I have to outperform
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him by
.
2φ J
σiJ
-
0
1
2φ
1
2φ J
J
A
B
Those who initially voted for B vote
now for A.
Application: Hotteling model
On the beach, the question asked by two ice creams sellers is: where to locate? Which price to
do?
If they both locate at the centre of the beach, they will attract a large number of customers but
there will also be a strong competition. One way to break this competition is to move from the
center.
They will locate like this:
0
¼=A
¾=B
1
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People exactly in between will look at the price. If A increases his price, he will not loose the
extreme customers but the customers in the centre.
It is the same explanation for the votes: when you start to do better, you attract voters of the
other.
If φJ tends to zero, the denominator of
1
2φ
J
decreases and so
1
2φ
J
increases (and so does the
distribution). If φJ is small, it means that many people have extreme ideological points of view.
For the politicians, it means that they have to do far better than the other party to catch a lot of
people who initially voted for the other party.
σiJ
-
0
=
neutral
1
2φ
J
Biased towards A
1
2φ J
Biased towards B
If φJ is big, the distribution looks like that:
-
1
2φ J
Biased towards A
0
=
neutral
1
σiJ
2φ J
Biased towards B
It means that no one is strongly ideological attracted: people only care about policy and not a lot
about ideology.
What about δ?
δ is a shock, the “last-day-scandal”. It doesn’t depend on i or J meaning that it is the same for all
the voters.
δ


~ U − 1 , 1 
 2
 ψ
2ψ 
If ψ is small, it means that the distribution of the scandal is narrow.
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Timing of the game:
1
Candidates
announce
platforms
2
δ is realised
3
Elections
4
The winner
implements
his policy
Three steps to resolve the model:
1. Identify the swing voter (the guy who is indifferent between voting for A and B) in each group
J.
σiJ = WJ(gA) - WJ(gB) - δ ≡ σJ
σiJ
σJ
0
Vote for A
Vote for B
∀i with σiJ ≤ σJ votes for A.
Explanation: all people until σJ are voting for A.
2. Calculating vote share and probability of winning for each party.
A: Pr (σiJ ≤ σJ) =
this can be more or less than 50%.
Total vote share (VS) of A:
Each group has a size of
and
Probability of winning for A = probability that my VS is larger or equal than ½.
Pa = Pr [
]
Pa = Prδ
Pa=Prδ
With
average ideology.
Pa = Prδ
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δ
-1/2ψ
0
1/2ψ
Probability that δ falls in the interval?
With this expression, we can calculate how
increases if we increase gA.(It is symmetric for B).
To find the probability that party A wins the elections, we have to maximize this expression.
It is continuous in gA so it is differentiable.
3. Find the Nash equilibrium in platforms (gA, gB).
Seeing that it is symmetric, they will announce the same policy.
where
Utility of voter i :
FOC:
Result of probabilistic voting
Results of Downsian competition:
Outcome of the median voter
Comparison:
In the probabilistic voting model, we take the average income.
The group that is taking more weight is the group with higher and . Larger means larger
group and a larger means that, when A and B want to win the elections, they have to target the
group which is more likely to change his vote, the group that is the most ideologically mobile
( = ideology mobility). median voter is not he only thing that matters.
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Summary: Rising Inequality and the Politics of Redistribution in Affluent Countries
By Lane Kenworthy and Jonas Pontusson
In this paper, the authors try to measure the trends in inequality and in redistribution in several
OECD countries and the link between these two trends. According to the Downsian model if
there is more inequality in a country, there will also be more redistribution in this country.
Trends in inequality:
The evolution in each country depends on the measures (if we use individual earning or workingage household income). For instance in some countries (Netherlands), the inequality among
working-age household decreases during the studied period but it’s not the case among full-time
employed individuals. For others (Finland), it’s the opposite. This can be explained by different
factors such as marital instability, the increasing number of single-headed households and
employment evolution. For instance, in countries with better employment performance, lowearning households benefited relative to high-earning ones but not in countries with poor
employment performance.
Moreover, “patterns of self-employment may account for some of the differences between trends
in individual earnings inequality and household income inequality”.
Trends in redistribution:
What matters for individuals is not the market income but the disposable income (market income
+ transfers – taxes).
In order to measure the redistribution, they use the absolute difference between the Gini
coefficients of disposable income and market income for working age household (excluding from
consideration the pensions which represent the largest budget program). The redistribution has
increased in almost all countries. For Bradley and colleagues, “countries in which Left parties
have participated in government over extended periods of time tend to have more redistributive
tax and transfer systems”. However, it seems that in some countries this trend of increase started
before Left parties gained control of government. In addition, some countries such as Germany
didn’t go through this Left-party dominance whereas they have a more redistributive system.
Almost all the increase is attributed to transfer payments (due to the labour market development).
Indeed, the rising unemployment (especially among less educated workers) leads to the
distribution of more unemployment compensation and other transfers.
The effect of market inequality on redistribution
Median voter’s theorem says that the median voter’s preference for redistributive policy is a
function of the distance between the median voter’s income and the average income.
If inequalities increase, this distance between the median voter’s income and the average income
also increases, and support for government spending increases too. As a consequence, countries
with unequal distributions of market income (so high inequality) should exhibit higher levels of
redistributive spending than the others with less inequality. However, the opposite is verified in
the data’s: countries with more egalitarian earnings distributions tend to have larger welfare states
than countries with more inegalitarian wage structures. This is the “paradox of redistribution”.
This paradox is explained by Moene and Wallerstein who highlight the fact that government
spending not only redistributes income, but also provides insurance. The higher is the income,
the more you want insurance, holding risk constant..People with higher incomes will choose to
buy more insurance against income loss than people with lower incomes. As inequality increases,
the median voter income decreases and his willingness of social insurance too (he will vote for
less social policies with less redistribution).
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However, if we use the change in redistribution against changes in household market inequality, it
supports the Downsian model: the more inequality you have in one country, the more
redistribution there is.
Conclusion:
The trend in inequality is different depending on which measure we use (individual earning or
working-age household income). However, the redistribution has increased in almost all countries
and it’s mostly due to an increase in transfer payments (linked with a rising unemployment). The
relation between these two trends is ambiguous: as we use different measures, we have different
results. The Downsian model is verified if we use data’s based on household income.
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