Lesser of 2 evils

[Steve Eppley]

Bruce A wrote:
-snip-
>I don't think that "two evils" is intended to be important ONLY when
>such ties are occurring.
-snip-

Right, it's not related to pairwise ties.  It's about the dilemma
faced by some voters, who have more than one goal when voting.  
They want: 
1. to elect (one of) their favorite candidate(s).  
2. to defeat some candidates.  
3. the true strength of their favorite candidates to be known (even
  if these candidates aren't winners) in order to affect the perceived 
  mandate of the winner and to affect these candidates' (or their 
  parties') chances in future elections.  (I.e., they want to be able
  to vote sincerely for their favorites.)

The lesser of evils dilemma is about forcing voters to choose to 
abandon some of these goals, when there is no way to vote a ballot 
that furthers all three.

This November there will be a vote-for-only-one election here in
California between Clinton, Dole, Nader, and a few other candidates.
Of these three, I rank N>C>D.  If the pre-election polls indicate
Clinton has California's electoral college votes locked up, then
maybe I'll vote for Nader even though he doesn't have a chance to
win, since the numbers will have other future effects besides
determining the winner of this one election.  However, if there are 
many Californians like me who do this, the Clinton "lock" may be 
illusory and Dole could win.  A dilemma...  Also, suppose the 
pre-election polls show a close race between Clinton and Dole.
Then I'd probably vote (insincerely) for Clinton, discarding all 
goals except defeating the "worse of evils" Dole.  The dilemma 
is about the choice of goals to discard.

Mike O's conjecture(?) is that by using Condorcet the voters will be
free to vote in such a way--sincerely--that they won't have to
choose to discard any of their 3 goals, except in implausible 
scenarios.

Bruce's analysis certainly ignores goal number 3, by focussing only 
on the winner of the election at hand.

-snip-
>However, "two evils" necessarily requires that, in this very same
>election, it must also be simultaneously possible for the V(B,C)
>voters to cast their ballots such that:  1) none of them casts a
>"partially reversed" ballot, 2) none of them casts a ballot that
>ties B with an alternative ranked below B in the voters true
>preferences, and 3) C cannot win no matter how the W(C,B) voters
>cast their ballots.
-snip-

Why claim that the LOE dilemma requires *all* voters to have a
dilemma?  (Or have I misunderstood the analysis?)  It's a serious
problem even if only some voters have the dilemma.

Here's an example of the LOE dilemma in Copeland (and Regular-Champion, 
similar to Copeland).  It ought to look familiar:

Suppose the pre-election polls aren't precise, but show D with a 
plurality something like this:
  46 +-3:  D >> C&N
  20 +-3:  C >> D&N
  34 +-3:  N >> C >> D
(The '&' doesn't mean '=' here.  It means "is close to" and could be 
voted as any of '>', '<', or '='.  The '>>' means "is much preferred to."
Numbers are in millions.)

The 34M each have a choice to make.  If they go ahead and vote N>C>D
they can anticipate a circular tie (D>N>C>D).  If the tie-breaker is 
Copeland or Regular-Champion, D would win thanks to D's plurality.  
But one of the goals of the 34M is to defeat D.  

Suppose the poll was quite accurate regarding the 46 and 20 groups:
they vote all their '>>' preferences as '>'.
Suppose the 46M do indeed truncate their ballots (effectively to D>C=N).
Suppose the 20M do indeed truncate (effectively to C>D=N).
  Voting            34:    34:    34:
  Method           N>C>D  N=C>D  C>N>D 
  ---------------  -----  -----  -----
  Condorcet:         C      C      C
  Regular-Champion:  D      C      C

I haven't marked gains due to manipulation with [] brackets 
because there's doubt about whether the D win should or should not 
have brackets--there's so much truncation going on.  However, it's
clear that since C wins across the board in Condorcet, there's no 
gain by the 34M if they manipulate.  So they are free to vote 
sincerely in Condorcet in this example, whereas in Regular-Champion 
they have a dilemma about which goal to discard.

Here's another example, where there are fewer N supporters but some
(all? hard to say with inaccurate polling) of the D supporters
reverse to D>N>C to try to defeat C:
  The poll:
  46 +-3:  D >> C&N
  34 +-3:  C >> D&N
  20 +-3:  N >> C >> D

  The vote:
  46: D>N>C
  34: C
  20: ?  

20: N>C>D             20: N=C>D                   20: C>N>D
 D>C 46                D>C 46                      D>C 46
 C>D 54*               C>D 54*                     C>D 54*
 D>N 46*               D>N 46*                     D>N 46
 N>D 20                N>D 20                      N>D 20
 C>N 34                C>N 34                      C>N 54*
 N>C 66*               N>C 46*                     N>C 46
Condorcet: N          Condorcet: C and N tie      Condorcet: C
Reg-Champ: D          Reg-Champ: D                Reg-Champ: C

The resolution of the tie between C and N in the N=C>D column would
depend on the choice of tie-breaker.  C would win if the tie-breaker
is plurality.  (If a Condorcet+NOTB ballot is used, the tie-breaker
could be Most_Approved: NOTB>A means "A is disapproved" and A>NOTB
means "A is approved.")  More likely, though, there wouldn't be a tie
in such a large election because none of the subgroups would
manipulate on *all* of their ballots.

It's clear that the 20M N supporters won't gain by manipulating here
if Condorcet is used, so they have no dilemma and will vote N>C>D. 
But they can gain if Regular-Champion is used.  So in Regular-Champion
they have a dilemma, a choice between showing their true support for
N or defeating D.

Imho, society should use a voting method which minimizes the
incentives to manipulate one's vote so we can better determine the
true will of the people.  This standard is important to me, and I'd
hope it's important to many.  It's intimately connected with the LOE 
dilemma.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)