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Veto Players

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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

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**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 I SQ P S

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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

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**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 C B A SQ

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**Winset of SQ for two veto players A and B**

for A and B

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**A change of rule: SMR and unanimity winsets**

B C Unanimity winset SQ

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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

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**Unanimity core and W (SQ)**

Unanimity core (Pareto set) A B C W(SQ) SQ

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**Status quo inside the core**

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 A B C SQ

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**Status quo outside the core**

B C SQ W(SQ) is not empty VPs can find alternatives that they all prefer to the SQ The sufficient condition for change is satisfied, the SQ is not a stable equilibrium

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**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

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**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. 13 13

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**SQ and stability Ideal points of A, B and C and core**

SQ1 inside the core winset is empty SQ1 C B A SQ2 outside the core, winset is not empty SQ3 farther away from the core, winset is larger

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**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

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**Winset and core with a new VP**

With three VP, the triangle is the core and the orange area the winset A new veto player D increases the core ... And decreases the winset

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**A new (not influential) veto player**

Since D is inside the core of A,B e C, the core does not increase, and the winset does not reduce B C A D E Same for E SQ These veto players are absorbed

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A particular case Since D is outside the core of A,B and C, D increases the core B C A D This could increase stability by ... SQ … the winset of that particular SQ, is not reduced, hence stability given this SQ is unaffected

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**A VP that changes preferences**

As C moves away, the core increases ... B A C0 … and W(SQ) get smaller C1 SQ

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**The number of veto players is not the crucial element**

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

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**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

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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 |SQ-SQ’| SMALL LARGE SMALL W(SQ)

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Issue 1 x A B x’ Issue 2 X’ is unanimously preferred by A and B to x. The line between A and B is A Pareto set (or Unanimity Core)

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**B1 A B1 B1 SQ ranking A B 1° 2° B1 A1 3° 4° SQ 5°**

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 B1 A ranking A B 1° 2° B1 A1 3° 4° SQ 5° B1 B1 SQ

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**A1 B A1 A1 SQ ranking A B 1° 2° B1 A1 3° 4° SQ 5°**

if B controls the agenda he can win A1. However differently from the instability example, now : Control of agenda means also excluding some alternatives (A1 or B1) from the set of available alternatives The agenda setter cannot win its best alternative (A or B) A1 B ranking A B 1° 2° B1 A1 3° 4° SQ 5° A1 A1 SQ

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**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

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

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

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**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

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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

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**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

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**The core and the winset when there is the unanimity rule**

A, B, C are member of a collective veto player and SQ is the status quo SQ A B C This is the unanimity core This is the winset in the same circumstance If the collective veto player adopts the unanimity rule then it happens what we have already seen with 3 individual veto players

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**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

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**Different decision rules: winset**

A collective veto player composed of 5 individuals Winset in case of unanimity (brown) SQ Winset in case of qualified majority (4/5) (brown+orange) Winset in case of simple majority (brown+orange+yellow)

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**Different decision rules: core**

Unanimity Core (light grey pentagon+dark grey small pentagon) SQ Qualified majority (4/5) Core Dark grey small pentagon If the decision rule is the majority then the core is empty

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**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

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**Wincircle of the status quo**

First step You have to draw the medians of the collective veto player SQ

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**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. Y r

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**Wincircle dello status quo**

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

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**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. SQ Y r d

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Radius d+2r winset yolk wincircle

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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

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1 5 6 SQ d+2r d+2r 2 3 4

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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

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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: 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 Policy Stability decreases as the q-cohesion of a collective player increases Policy stability increases or remains the same as the required qualified majority threshold q increases.

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