Democratic Stability

1
Democratic Stability

• Lecture 6

2
Outline

• What is democracy?
• Madison on democracy
• Schumpeter on democracy
• The 2004 Ukrainian presidential elections
• Democracy as a repeated game
• Democratic stability as a Nash equilibrium
• Substantive Implications
• Implications for Iraq
• Informal Extensions

3
What exactly is democracy?

• Democracy is a system of repeated elections.
• The system of repeated elections has two
  functions
• (a) it allows voters to control politicians
• (b) it allows for a peaceful transfer of power

4
Madison on democracy
... the House of Representatives is so
constituted as to support in the members an
habitual recollection of their dependence on the
people. Before the sentiments impressed on their
minds by the mode of their elevation can be
effaced by the exercise of power, they will be
compelled to anticipate the moment when their
power is to cease, when their exercise of it is
to be reviewed, and when they must descend to the
level from which they were raised there forever
to remain unless a faithful discharge of their
trust shall have established their title to
renewal of it. Federalist Papers p. 352
5
Schumpeter on democracy
the classical theory centered on the
proposition that the people hold a definite and
rational opinion about every individual question
and that they give effect to this opinion by
choosing representatives who will see to it
that that opinion is carried out. Thus the
selection of representatives is made secondary to
the primary purpose of the democratic
arrangement which is to vest the power of
deciding political issues in the
electorate. Suppose we reverse the roles of these
two elements and make the deciding of issues by
the electorate secondary to the election of men
who are to do the deciding. And we define the
democratic method is that institutional
arrangement for arriving at political decisions
in which individuals acquire the power to decide
by means of a competitive struggle for the
peoples vote.
6
The Puzzle?

• Assume that elections are an institutional
  mechanism for a peaceful alternation of power.
• Why are individuals who lose an election, willing
  to give up power rather than stage a coup or
  organize a revolution?

7
2004 Ukrainian presidential elections

• Viktor Yuschenko challenged incumbent prime
  minister Viktor Yanukovitch.
• Failed-poison attempt

• and
  state-sponsored electoral fraud triggered a
  popular uprising (Orange Revolution).
• Yanukovitch and incumbent president Leonid Kuchma
  chose between
• staging a military coup
• or letting the Court decide.

8
Democracy as a repeated game

• There are two players, A and B.
• t 0,1,2,3 denotes an electoral cycle.
• There is 1/2 chance that a player wins at t.
• The winner receives 1 and does nothing.
• The loser decides whether to accept the defeat or
  stage a coup.
• If loser accepts, he gets 0 and the game
  continues.
• If loser stages a coup, the game ends in a civil
  war.
• There is a q chance that a player wins the war.
• A player gets 1-c for ever if he wins the war,
  and 0 if he loses (c stands for the cost of
  dictatorship).
• k is the probability that the game goes on for
  another round.

9
The Extensive Form of Game

• An extensive form of a game is a graphical
  representation of that game as a game-tree.

10
Game tree
N
stands for Nature
½ A loses (B wins)
N
½ A wins (B loses)
q
1-q
coup
coup
A
B
N
N
1-q
q
respect
respect
N
N
k
1-k
N
N
½ A loses (B wins)
½ A wins (B loses)
11
Histories and Strategies

• Let Xi R, C be the action set of player i at
  each period t
• Let ht (R)0, (R)1, (R)t-1 be the history of
  the game up to but not including period t.
• A strategy si for player i specifies an action
  after every history of the game.
• Example Always respect elections

12
Stability as a Nash Equilibrium

• sA always respect elections
• sB always respect elections
• Democracy is stable if both players always
  respect elections.
• Democracy is stable if the strategy profile (sA,
  sB) is a Nash equilibrium

13
Assume A loses what are the incentives not to
deviate for player A?

• EuA(sA) 0 k (½½0) kk (½½0)
• k/2(1-k)
• EuA(sA) q(1-c)k(1-c)... (1-q)0 k0
  ...
• q(1-c)/(1-k)
• EuA(sA) gt EuA(sA)
• ? k/2(1-k) gt q(1-c)/(1-k)
• ? Condition 1 Player A does not deviate if
• q lt k/2(1-c)

14
Assume B loses what are the incentives not to
deviate for player B?

• EuB(sB) 0 k (½½0) kk (½½0) ...
• k/2(1-k)
• EuB(sB) (1-q)(1-c)k (1-c)... q0k0...
  
• (1-q)(1-c)/(1-k)
• EuB(sB) gt EuB(sB)
• ? k/2(1-k) gt (1-q)(1-c)/(1-k)
• ? Condition 2 Player B does not deviate if
• q gt1- k/2(1-c).

15
The Range of Democratic Stability

• Condition 1 q lt k/2(1-c).
• Condition 2 q gt 1- k/2(1-c).
• Jointly k/2(1-c) gt q gt 1- k/2(1-c).

A deviates
B deviates
RANGE OF STABILITY
q


1
0
16
Implications for the Ukraine

• 1) Democratic stability requires a rough balance
  of power (q close to ½)
• 2) Democratic stability requires a stable
  international environment (high k)
• no risk of Russian intervention
• 3) Democratic stability requires that
  dictatorship be costly (high c)
• International sanctions

17
Democratic Culture and Iraq

• If democratic culture means that all politicians
  are willing to respect elections, then stable
  democracy leads to democratic culture and not the
  other way around.
• An important implication of this result is that
  it should be possible to build a stable democracy
  in Iraq even though that country has no history
  and thus no culture of democracy.

18
Possible Extensions

• What if the probability that a player wins and
  election is not equal to ½?
• What is the payoff for losing the civil war is
  worse than the payoff for losing an election?
• What if there are three players rather than just
  two?