# [EM] SODA and the Condorcet criterion

fsimmons at pcc.edu fsimmons at pcc.edu
Thu Aug 4 14:33:04 PDT 2011

```I want to thank Jameson for taking the ball and running with it on SODA.  I really appreciate his talented
and energetic work on elaborating, explaining, and selling the method.

It's exciting to me to see the possibilities.

Here's more evidence of monotonicity:

With a three candidate cycle

x A>B>C
y B>C>A
z C>A>B

if x>y>z, then A plays first, but B wins the election.

If the B faction increases at the expense of the x faction so that  y>x>z, then B goes first, and still wins!
(because ACB is opposite the cyclic order of the beat cycle)

The other nice thing about SODA and strong first play order is that it makes the game of chicken go
away.

> Date: Thu, 4 Aug 2011 08:01:30 -0500
> From: Jameson Quinn
> To: EM
> Subject: [EM] SODA and the Condorcet criterion
> Message-ID:
>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Here's the new text on the SODA
> page> Delegated_Approval#Criteria_Compliance>relatingto the Condorcet
> criterion:
> It fails the Condorcet
> criterion,
> although the majority Condorcet winner over the ranking-
> augmented ballots is
> the unique strong, subgame-perfect equilibrium winner. That is
> to say that,
> the method would in fact pass the *majority* Condorcet winner
> criterion,assuming the following:
>
> - *Candidates are honest* in their pre-election rankings.
> This could be
> because they are innately unwilling to be dishonest, because
> they are unable
> to calculate a useful dishonest strategy, or, most likely,
> because they fear
> dishonesty would lose them delegated votes. That is, voters
> who disagreed
> with the dishonest rankings might vote approval-style instead
> of delegating,
> and voters who perceived the rankings as dishonest might
> thereby value the
> candidate less.
> - *Candidates are rationally strategic* in assigning their
> delegated vote. Since the assignments are sequential, game
> theory states that there is
> always a subgame-perfect Nash equilibrium, which is always
> unique except in
> some cases of tied preferences.
> - *Voters* are able to use the system to *express all relevant
> preferences*. That is to say, all voters fall into one of two
> groups: those who agree with their favored candidate's
> declared preference order and
> thus can fully express that by delegating their vote; or
> those who disagree
> with their favored candidate's preferences, but are aware of
> who the
> Condorcet winner is, and are able to use the approval-style
> ballot to
> express their preference between the CW and all second-place
> candidates. "Second place" means the Smith set if the
> Condorcet winner were removed from
> the election; thus, for this assumption to hold, each voter
> must prefer the
> CW to all members of this second-place Smith set or vice
> versa. That's
> obviously always true if there is a single second-place CW.
>
> The three assumptions above would probably not strictly hold
> true in a
> real-life election, but they usually would be close enough to
> ensure that
> the system does elect the CW.
>
> SODA does even better than this if there are only 3 candidates,
> or if the
> Condorcet winner goes first in the delegation assignment order,
> or if there
> are 4 candidates and the CW goes second. In any of those
> circumstances,under the assumptions above, it passes the
> *Condorcet* criterion, not just
> the majority Condorcet criterion. The important difference
> between the
> Condorcet criterion (beats all others pairwise) and the majority
> Condorcetcriterion (beats all others pairwise by a strict
> majority) is that the
> former is clone-proof while the latter is not. Thus, with few
> enough strong
> candidates, SODA also passes the independence of clones
> criterion
> .
>
> Note that, although the circumstances where SODA passes the Condorcet
> criterion are hemmed in by assumptions, when it does pass, it
> does so in a
> perfectly strategy-proof sense. That is *not* true of any actual
> Condorcetsystem (that is, any system which universally passes
> the Condorcet
> criterion). Therefore, for rationally-strategic voters who
> believe that the
> above assumptions are likely to hold, *SODA may in fact pass the
> Condorcetcriterion more often than a Condorcet system*.
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