[EM] Participation & SARC

[Markus Schulze]

Dear Steve,

you wrote (5 May 2000):
> The wording of the participation criterion by Herve Moulin 
> (Axioms of Cooperative Decision Making, Cambridge University 
> Press, 1988, p.239) refers to a single voter, not a group:
>
>   Participation: Say that candidate a is elected from the set A
>   by the electorate N.  Next consider a voter i outside N. 
>   Then the electorate N U {i} should elect a or some candidate
>   whom agent i strictly prefers to a.

Actually, it doesn't matter whether you are talking about a
single voter or a same-voting group of voters.

1. If a single voter cannot be punished for voting, then also
a same-voting group of voters cannot be punished for voting.
The reason: You can simply take one voter of this group after
the other. If the same-voting group worsened the result of
the elections, then -when you take one voter of this group after
the other- at least one voter of this group would worsen the
result of the elections.

2. If a same-voting group cannot be punished for voting, then
also a single voter cannot be punished. The reason: Every voter
forms a group of one voter.

Therefore, Herve Moulin's definition and my definition of
participation are identical. By the way: In "Condorcet's Principle
Implies the No Show Paradox" (Journal of Economic Theory, vol. 45,
p. 53-64, 1988), Moulin always uses same-voting groups to prove
a violation of participation.

******

You wrote (5 May 2000):
> A criterion like SARC seems better than participation when the 
> voters are sophisticated (and unconstrained by accountability, 
> e.g., secret ballot), since it is unreasonable to compare only 
> sincere voting and the abstention strategy when other strategies 
> may be better than both of those.

The problem is: To be able to compare sophisticated outcomes, you
have to make presumptions about the used strategies. It is not
easy to make non-trivial justifiable realistic presumptions
about the used strategies.

******

You wrote (5 May 2000):
> For participation to be considered an important criterion in 
> large public elections, wouldn't there need to be empirical 
> evidence that significant numbers of voters will routinely not 
> vote due to a procedure's failure to rigorously comply with 
> participation?  (Voter turnout might actually increase overall, 
> given a procedure which fails participation but does a good job 
> of solving other problems like spoiling.)  Also, is there a 
> plausible argument that society would be worse off using a 
> procedure which doesn't rigorously comply with participation?

Supporters of Alternative Voting usually claim that Alternative
Voting guarantees that a set of additional voters each with the
same sincere opinion can never be punished for going to the
polls and voting sincerely. They claim that -as Alternative
Voting guarantees that a vote of a given voter for a given
candidate will never be counted unless all those candidates who
are prefered to this given candidate by this given voter cannot
be elected any more- a voter cannot be punished for making an
additional preference. And they claim that this means that
an additional voter cannot be punished at all for going to
the polls and voting sincerely.

The participation criterion is the mathematical formulation of
the claimed property of Alternative Voting.

Independently on whether you think that a given property is
important, you have to find a mathematical formulation of this
property to be able to discuss it in a non-trivial manner.

******

You wrote (5 May 2000):
> I haven't seen any messages posted by Lucien in years.  Is it 
> correct to use the present tense when describing his advocacy?

Lucien Saumur still promotes Smith//RandomCandidate.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de