Veto Players

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
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
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
6
Winset of SQ for two veto players A and B
winset of SQ for A and B
7
A change of rule SMR and unanimity winsets
SMR winset
Unanimity winset
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)
Unanimity core (Pareto set)
W(SQ)
10
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
11
Status quo outside the core
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
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 well 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.

13
14
SQ and stability
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
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
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
17
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
Same for E
These veto players are absorbed
18
A particular case
Since D is outside the core of A,B and C, D
increases the core
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
As C moves away, the core increases ...
and W(SQ) get smaller
20
The number of veto players is not the crucial
element. The distances make the difference
WA
WB
21
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

22
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)
23
Issue 1
x
B
A
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)
24
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
A
B1
ranking A B
1 A B
2 B1 A1
3 A1 B1
4 SQ SQ
5 B A
B1
B1
SQ
25

• 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)

B
A1
ranking A B
1 A B
2 B1 A1
3 A1 B1
4 SQ SQ
5 B A
A1
A1
SQ
26
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

27
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 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
28
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

29
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

30
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

31
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
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
32
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
33
Different decision rules winset
A collective veto player composed of 5 individuals
Winset in case of unanimity (brown)
Winset in case of qualified majority (4/5)
(brownorange)
Winset in case of simple majority (brownorangeye
llow)
34
Different decision rules core
Unanimity Core (light grey pentagondark grey
small pentagon)
Qualified majority (4/5) Core Dark grey small
pentagon
If the decision rule is the majority then the
core is empty
35
(No Transcript)
36
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

37
Wincircle of the status quo

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

38
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.

39
Wincircle dello status quo

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

40
Wincircle dello status quo

• Fourth step
• The circle with th center Y and the radius d2r
  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.

41
Radius d2r
winset
yolk
wincircle
42
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

43
1
5
6
SQ
d2r
d2r
2
3
4
44
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
45
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.