1

Veto Players

2

Veto player

Veto players are individual or collective actors whose approval is necessary to change the status quo

In political systems we have Institutional veto players: parliamentary assemblies,

constitutional courts etc. Partisan veto players: government coalition parties

We generally consider veto players with single-peaked Euclidean utility functions in a uni- or bi-dimensional space

Hence, we have circular indifference curves in a bi-dimensional space with respect to a status quo policy

3

I

SQP

S

Preferences for reform

Veto player I accepts to change the SQ only if the alternatives are in the colored area

For instance, it will accept policy P but rejects policy S

4

Winset of SQ

It is the set of alternative policies that can beat the status quo

For a single veto player, it is the set of the alternatives inside the circle centered on the ideal point and passing through the SQ

For more veto players it is the intersection of these circles

5

SQA

B C

Winset(SQ) for three veto players A, B and C

W(SQ) for the three VPs is the colored area closer to the three ideal points than the SQ

If W(SQ) is empty, the political system does not allow reform

6

Winset of SQ for two veto players A and B

A

SQ

B

winset of SQ

for A and B

7

SQ

A

B

C

A change of rule: SMR and unanimity winsets

SMRwinset

Unanimitywinset

8

Unanimity Core

Sets of points that cannot be beaten if decisions are taken by unanimity

It is the Pareto set It is the smallest convex polygon with angles

on VPs ideal points The core does not depend on the SQ, but only

on the VPs ideal points

9

Unanimity core and W (SQ)

A

B

C

SQ

Unanimity core (Pareto

set)

W(SQ)

10

Status quo inside the core

A

B

CSQ

W(SQ) is empty

No policies are preferred to the SQ by all the three VPs

The necessary condition for change is not satisfied stability

11

Status quo outside the core

W(SQ) is not empty

VPs can find alternatives that they all prefer to the SQA

B

C

SQ

The sufficient condition for change is satisfied, the SQ is not a stable equilibrium

12

Winset, core and policy stability

The dimension of the W(SQ) and of the core are proxies for policy stability

W(SQ) is negatively related to stability Core is positively related to stability Additionally, the farther the SQ is, the more likely

we’ll have significant policy change Stability is function of the SQ and its position

relative to that of the VPs ideal points

13

Unanimity Core and Winset : a comparison

Winset of the status quo is a more reliable proxy of the real policy stability. When the winset is very small it is highly likely that not policy change takes place because of the transaction costs. The size of the winset tell us also if we are dealing with an incremental change or a major policy change.

Unanimity core is a measure independent of the position of the status quo. Sometimes is not easy to locate the status quo. Moreover political analysis based upon status quo position has an extremely contingent and volatile character. If you want to assess some stable and general features of the political systems unanimity core is the best measure.

14

SQ1 SQ2 SQ3

C

B

A

Ideal points of A, B and C and core

SQ1 inside the core winset is empty

SQ2 outside the core, winset is not empty

SQ3 farther away from the core, winset is larger

SQ and stability

15

Adding a new VP, winset and core

If we add a VP, winset is likely to get smaller (and the core to get bigger) because the new VP can veto alternatives that were accepted by the existing VPs

But if no new alternatives are blocked by the new VP, the winset (and the core) does not change

Hence, adding a new VP either increase stability (winset is smaller and core larger) or does not make any change

16

Winset and core with a new VP

A new veto player D increases the core ... And decreases the winset

With three VP, the triangle is the core and the orange area the winset

17

A new (not influential) veto player

SQ

D

B

CA E

Since D is inside the core of A,B e C, the core does not increase, and the winset does not reduce

Same for E

These veto players are absorbed

18

A particular case

SQ

B

CA

Since D is outside the core of A,B and C, D increases the core

D This could increase stability by ...

… the winset of that particular SQ, is not reduced, hence

stability given this SQ is unaffected

19

A VP that changes preferences

C1

B

AC0

As C moves away, the core increases ...

… and W(SQ) get smaller

SQ

The number of veto players is not the crucial element. The distances make the difference

WBWA

New veto players, distances among veto players and policy stability Absorption rule: If a new veto player is added within the

unanimity core of any set of previously existing veto players, this new veto player has no effect on policy stability

Quasi-equivalence rule: For any set of existing veto players , the necessary and sufficient condition for a new veto player not to affect the winset of any status quo is that the new veto player is located in the unanimity core

…However for some specific status quo the new veto player can be outside the unanimity core and not affect the policy stability.

Distances among vetoplayers: If Ai and Bi are two sets of veto players and all Bi are included inside the unanimity core of the set Ai, then the winset of Ai is included in the winset of Bi for every possible status quo and viceversa

The size of the Winset of SQ, W(SQ), is a necessary but not sufficient condition for having a (big) policy change (|SQ-SQ’|). If the Winset is small the change will be small (or absent). If the Winset is big the change can be big or small (or absent). However on average the size of the change should

increase with the size of the Winset. LARGE

SMALL

|SQ-SQ’|

W(SQ)LARGE SMALL

Issue 1

Issue 2

A B

x

x’

X’ is unanimously preferred by A and B to x. The line between A and B isA Pareto set (or Unanimity Core)

Previous picture helps to illustrate that the control of agenda is important also when there is not instability (a cycle) and the voting rule is the unanimity rule. Two political actors and 5 alternatives; if A controls the agenda he can win B1

ranking A B

1° A B

2° B1 A1

3° A1 B1

4° SQ SQ

5° B A

B1 A

B1

SQB1

if B controls the agenda he can win A1. However differently from the

instability example, now :1) Control of agenda means also

excluding some alternatives (A1 or B1) from the set of available alternatives

2) The agenda setter cannot win its best alternative (A or B)

ranking A B

1° A B

2° B1 A1

3° A1 B1

4° SQ SQ

5° B A

A1 B

A1

SQA1

Agenda Setting Power and stability

A single veto player is also the agenda setter and has no contraints in the selection of outcomes

The significance of agenda setting declines as policy stability increases

The significance of agenda setting increases as the agenda setter is located centrally among existing veto players

Agenda setting power, number of veto players and location in the political space

If the agenda setter was more centrally located as regards the other veto players, it could choose best alternatives (and sometimes even its idela point) as Z, that is insed the winset of A and B

Z

if X has agenda setting power and A is the only other vetoplayer, X can choose X1

If also B is a vetoplayer, then X will choose X2, That cannot be closer to X than X1.The advantage from having agenda setting power decreases with more veto players

The veto players are mostly collective..

Many veto players are in fact composed of many individuals: they are collective veto players

Examples: Legislative assemblies, parties etc. Upper Chamber can prevent the final approval of a bill

already passed in the lower Chamber A party can be numerically necessary to support a

government

The decisional rules in force in each collective veto player affects the final outcome

Two Problems

It is much more difficult to identify the winset of a collective veto player. When the veto players are more than one, the final identification of the winset is even more difficult.

If the collective veto player takes decisions using a simple majority rule then there is the possibility of cycling majorities, in other terms no equlibria

Decision rules and stability

Intuitions suggests that if the collective veto player choose with a simple or qualified majority the policy stability should decrease in comparison with the unanimity criterion

therefore the core should shrink The winset should expand

The core and the winset when there is the unanimity rule

This is the unanimity core

This is the winset in the same circumstance

A, B, C are member of a collective veto player and SQ is the status

quo

SQA

B

C

If the collective veto player adopts the unanimity rule then it happens what we have already seen with 3 individual veto players

The core and the winset when there is the simple majority rule

From the unanimity to the majority the winset expands..

..and the core becomes empty. It does not exist any point that belongs to all Pareto sets of all majority coalitions

Therefore when the veto player decides by using the majority rule is easier to agree to change the status quo

Different decision rules: winset

A collective veto player composed of 5 individuals

SQ

Winset in case of unanimity (brown)

Winset in case of qualified majority (4/5) (brown+orange)

Winset in case of simple majority(brown+orange+yellow)

Different decision rules: core

If the decision rule is the majority then the core is

empty

SQ

Unanimity Core (light grey pentagon+dark grey small pentagon)

Qualified majority (4/5) Core Dark grey small pentagon

Theoretical developments Even if it is difficult to identify the winset of the status quo

of a collective veto player, theorists have suggested a procedure to find a circle where the winset is included

Therefore even if the core is empty, it is possible to bound an area of the political space where there are the policies the collective veto player prefers to the status quo. While any policy inside this circle can defeat the status and can be defeated by some other policy inside the same circle, no policy outside the circle wins agaisnt the status quo

Wincircle of the status quo First step

You have to draw the medians of the collective veto player

SQ

Wincircle dello status quo Second step

Identification of the yolk (the smallest circle that touches all medians) and of its center Y il suo centro and its radius r.

SQ

Yr

d

Wincircle dello status quo Third step

Given the status quo SQ , d is the distance between Y and SQ

SQ

Yr

Wincircle dello status quo Fourth step

The circle with th center Y and the radius d+2r is the wincircle of the collective veto player, given the staus quo SQ

However not all points in the wincircle belong also to the winset. Belonging to the wincircle is necessary but not sufficient condition to defeat the status quo.

d

SQ

Yr

yolk

winset

Radius d+2r

wincircle

Radius and m-cohesion

The radius of the yolk of a collective veto players is an indication of its m-cohesion, or, in other terms , how well the majority is represented by the point Y located at the center of the collective veto player

As the radius decreases the m-cohesion of the collective veto player increases.( and the wincircle decreases).

Policy stability increases as the m-cohesion of a collective veto player increases (as the radius of the yolk decreases)

An increase in size of a collective veto player (in terms of members) coeteris paribus increases its m-cohesion and consequentely increases policy stability

1

2 3

4

5 6

d+2r

SQd+2r

When SQ is in the hatched area, change is not possible with individual VPs. It may be possible with collective VPs, but it will be incremental

Qualified majorities

Some collective veto players decide by using qualified majorities

U.S. Congress when they have to override the presidential veto (2/3)

Decisions of the UE Council of Ministers.( about 5/7) Also in this case is possible to identify a wincircle

However there are some very important differences:1. The more q-cohesive a collective veto player is (the smaller

the radius of the q-yolk) , the larger the size of the q-wincircle

2. Policy Stability decreases as the q-cohesion of a collective player increases

3. Policy stability increases or remains the same as the required qualified majority threshold q increases.