Median Voter Theorem Flashcards

1
Q

Single peaked preferences

A

Every individual has a most preferred alternative

(Like a predetermined position on a linear ordering) e.g music volume

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2
Q

If we restrict preferences, which assumption is violated

A

Unrestricted domain - i.e universality - have to consider all individuals

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3
Q

Draw spatial representation of single peaked preferences pg 7

Identify bliss point

A

X is bliss point (most preferred)
Z and Z’ and Y and Y’ are welfare decreasing

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4
Q

Pg 8 diagram of no single peaked preference

A
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5
Q

Criteria for single peakedness

A

Individual preferences have to be smooth ie should prefer closer to ideal point rather than further apart.

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6
Q

Are single peaked preferences realistic

A

Yes in most economic situations, individual preferences are single peaked and smooth

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7
Q

Benefit of single peaked preferences

A

Condorcet winner always exists

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8
Q

Overlapping preferences diagram pg 12

Where is the win set?

A

Each line presents different individual

Red horizontal line shows all positions red prefers over X
Green horizontal line shows all positions along line preferred over X
Black horizontal line shows all preferred positions over X

So thus win set is between X and Y - anywhere along that line will be preferred by all 3 individuals compared to initial point X

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9
Q

Assumptions for MVT (3)

A

Single peaked prefs
Single dimension (only considering 1 policy)
All individuals vote sincerely

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10
Q

2 types of elections

A

Voting directly on policy
Select political bodies to represent

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11
Q

For 2nd, more likely to base policy to court the vote of the median voter, and voters likley to base choices on preferences over the policy. When may voters deviate from this

A

They could consider additional factors e.g ideology or sympathy e.g prefer a candidate to another

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12
Q

Main implication/result of MVT

A

Convergence towards the median voter - parties adopt the same policy towards the preference of the median voter.

a1=a2=Xm
Xm is preference of median voter

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13
Q

Downsian police convergence theorem looked at why they converge.

What assumption needs to be made, and what happens

A

Assume median voter preference unannounced,

This means the party closest to median wins. Not stable, as other party has incentive to move closer to Qm to win. Keep converging and competing it towards the centre till both policies are the same

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14
Q

What is Downsian environment/opportunistic

A

Parties are only motivated by winning (do not care about policy, just want to win)

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15
Q

Payoff for parties

A

Probability of winning x benefit of winning
V = πa
π is probability of winning
a is benefit of winning

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16
Q

So the result is converged policies i.e α1=α2=Xm is a stable nash equilibrium.

Proof is as follows:
Reason 1: If both parties choose median voter position, no motivation to deviate. Why?

B) Reason 2: If both choose the same position but not median voter position, what happens?

C) Reason 3: if both choose different positions and neither of median voter position what happens

A

No motivation to deviate as expected return drops from half the benefits, to 0.

B)
Unstable - Deviation is beneficial - they can change outcome from a tie (in that position) to a win (by moving closer to the median voter)

C) incentive to deviate too - can change outcome from a loss to a win

17
Q

Given the payoff expression, what is the expected payoff for parties

A

V = πa

Since both pursue preference of MV, probability is 1/2

So payoff is 1/2a

18
Q

Applied example of MVT: redistributive taxation. Assume a income tax rate t and gov provides lump-sum transfer T for everyone. Assume costs of tax per person (for gov) are δt². Who wants the high tax rate? Poor or rich?

A

Poor prefer higher tax! The transfer is more beneficial to them, thus want a higher tax rate.

19
Q

Model set up
Agent maximises utility
Ui = Ci + T
Utility is consumption + transfer

What is the budget constraint and government budget constraint

B) What is lump sum transfer per person (hint: linked to government budget constraint

A

Ci <= (1-t)yi
Consumption has to be less/equal to disposable income i.e the budget constraint

Government budget constraint is just their income - costs
Σ tyi - δt²
(Sum of tax revenue from each individual - costs of taxing them

B)
T is the lump sum - which is just government budget divided by number of individuals (n)
T = R/n = tybar - δt²

20
Q

IMPORTANT FLASHCARD:
Find indirect utility function by subbing in lump sum (T) and Ci (our budget constraint) into the utility function U = Ci + T

B) If we then differentiate FIRST AND SECOND ORDER with respect to T, what does this help prove us?

A

Wi = (1-t)yi + tybar - δt²

B) differentiate twice get us
-2δ<0
Negative so proves there is maximum I.E SINGLE-PEAKEDNESS

THUS MVT APPLIES, WE WILL SEE CONVEGENCE

21
Q

We can also find the preferred policy of the median voter

What is their maximisation problem (similar to IO)

B) Then solve to find median voters optimal tax rate t

A

Max ui = Ci + T
Subject to budget constraint Ci <= (1-t)yi

B) use the indirect utility function and differentiate FOC, rearrange to find optimal t:
t*m = ybar - ym/2δ

22
Q

t*m = ybar - ym/2δ

What does this show

A

Tax will increase as the difference between average income (ybar) and median income (ym) increases (more income inequality, more tax for redistribution!!!)

23
Q

IRL do we observe higher or lower distributive tax compared to 1850.

A

Tax has increased: we have more redistribution

24
Q

So Meltzer and richards predict higher income inequality (ybar - ym) leads to more redistibution (higher t)

However little evidence of greater inequality increasing redistribution. Example

A

US is more inequal, and distributes less

compared to more equal EU countries, who distriubte more

25
Q

Do all citizens have equal influence on policy

A

Yes - in MVT, every voter is equal

No: if one dollar one vote. then sometimes privileged group can dominate: when income of this group increases, aggregate redistributive policies tild towards this group’s preferred policies

26
Q

Karabarbounis results on whether one dollar one vote exists i.e political influence increases with income

A

They find
As rich get wealthier, less redistribution
As middle class becomes wealthier, less redistribution
Key point: As poor gets wealthier, more redistribution

thus true, poor people vote and policy reflects their preference of wanting more redistirbution!political influence is increasing with income

27
Q

MVT drawbacks (4)

A

Requires odd number to ensure majority (if tie: theorem doesn’t help determine which will win)

One dimensional - IRL consider multiple policies

Only assumes 2 parties - with 3, no stable equilibrium since always incentive to move in response to opponents positions

Assumes parties only care about winning, irl may consider ideology and own views rather than primarily courting for the median voter preference

28
Q

Do policies reflect median voter iRL?

A

Mixed
Yes in policy where median voter can credibly understand and care about public policy e.g education,health etc
But in other policy areas e.g trade policy (MVT performs poorly, median voter may not care/understand)

29
Q

Real life example of MVT: Miller

A

Saw universal womens suffrage (right to vote) in US in 1920

Median voter bliss point adjusted to reflect women’s preferences (who care more about health expenditure)

correspondingly increase public health spending, esp hygiene campaigns, child mortality fell 8-15%