[EM] voter strategy & 2-party domination under IRV voting

[Dave Ketchum]

NOT at all clear that 2-party domination is as evil as some claim.

I claim for Condorcet that it is adequate - CERTAINLY:
      Better than Plurality, Approval, IRV, for it lets voters approve of 
more than one candidate, and indicate preference among those approved.
      Better than those for the array of vote summaries which can be 
published and show relative preferences among all candidates.
      Simpler rules than for many methods such as Range.

So, with a reasonably complete statement of preferences, parties can see 
and respond to voters' indicated preferences:
      Also a combination of third party votes getting results even without 
winning any elections - and winning elections when/if major parties get 
careless enough.

I GREATLY dislike insincerely ranking the two frontrunners max and min, as 
described below.  I certainly want to rank my PREFERRED candidate as max, 
and ranking the best frontrunner second will hurt that frontrunner little 
(unless my preference is a contender - in which case I want my preference 
up front).

Often I would not see the second frontrunner winning as a disaster, and 
would see no profit in doing my best to cause this one to lose.
---------------------

Trying to figure out what Warren says below:
      We are doing strategy for C backers.
      We estimate that C will do better than A on first round - thus 
eliminating A - but we predict that B will then beat C, which we do not want.
      If we C backers switch to backing A, we can make sure C loses and 
then, hopefully, A wins.

Looks curious to me:
      This B cannot win on first choice votes alone.
      With sincere voting, enough A voter second choices will be B for B 
to win.
      With some C backers insincerely voting for A, C will lose on first 
round and, hopefully, enough of the remaining C voters will have A as 
second choice for A to win.

For this to be worth the pain:
      B must not be able to win on first choice votes alone.
      But sincere voting puts C ahead of A, and enough A second choices go 
to B for B to win.
      Still, with enough insincere voting, A will beat what B gets from 
first choice plus C second choices.
      Seems to me Warren's probabilities had to strain MUCH to back his 
desires.

DWK

On Sat, 13 Aug 2005 10:31:27 -0400 Warren Smith wrote:

> 
> On the probability that insincerely ranking the two frontrunners max and min, is
> optimal voter-strategy in an IRV (Instant Runoff Votng) election.
> ----------Warren D. Smith Aug 2005----------------------------------------------
> 
> MATHEMATICAL MODEL: 3-candidate V-voter IRV elections
> with random voters (all 3!=6 permutations=votes equally likely).
> 
> QUESTION: Is there a subset of identically-voting voters, who, by changing their vote
> to rank the two "perceived frontrunners" max and min ("betraying" their 
> true favorite "third party" candidate) can make their least-worst frontrunner win
> (whereas, their true favorite cannot be made to win no matter what they do)?
> 
> THEOREM: The answer to the above question is "yes" with probability
> at least  25% = 1/4  in the V=large limit.
> 
> PROOF SKETCH:
> 1. Assume wlog that B is the name of the IRV-winner.
> 
> 2. Assume wlog that A is the name of the candidate with the fewest top-rank votes,
> i.e. the one eliminated in the first IRV round, so it comes down to B versus C.
> 
> 3. The probability in the V=large limit tends to 1 that all the pairwise
> victory margins are of order approximately sqrt(V), and that all the 6 kinds of voters 
> occur with counts approximately V/6 each, i.e. much larger than sqrt(V).
> 
> 4. With probability 50%, candidate B has the most top-rank votes.
> 
> 5. Given that (4) is true: with probability 50%, the B-C gap in top-rank vote count,
> exceeds the C-A gap in top-rank vote count.  9We are now down to probability 25%.)
> 
> 6. Choose a subset, of cardinality of order sqrt(V), of the voters of type "C>A>B".
> (More precisely, we must choose the cardinality*2 to lie above the
> previously-mentioned C-A top-rank vote count victory margin, but below the B-C margin.)
> If they betray their favorite C by insincerely switching to "A>C>B", 
> then A becomes the IRV (and Condorcet) winner,
> which from their point of view is a better outcome.
> Q.E.D.
> 
> STRENGTHENING:
> Note our "C>A>B"-type voter subset can argue that obviously, nothing they can do
> will elect C, since when they rank C top honestly that fails to do it. Therefore,
> their only chance for an improvement is to go for electing A.  And the only
> way they can try is to raise A in the rankings.  As we've seen, this reasoning
> yields success for them, at least 25% of the time.  However, given their preconception
> that C has essentially no chance (or anyway, a chance well below 25%) of victory, 
> it actually makes sense for them to rank A top 100%, not 25%, of the time, 
> even though we know this will only be successful for them with probability 25%.  
> Because given their belief C has no chance, this cannot hurt them - and they know there 
> is a 25% chance it will help them.  So we conclude from this that in fact, the "betray C"
> strategy is better or at least as good for them as honesty, 100% of the time.
> 
> SUMMARY:
> This discussion presumably is the underlying theoretical explanation
> for the fact that all three IRV countries (Australia, Malta, and Ireland)
> historically have been 2-party dominated.
> 
> Eveidently the IRV voting method leads to 2-party domination, just like the flawed 
> plurality system that method was supposed to "fix."
> 
> So anybody who is interested in third parties ever having a chance, would
> be advised NOT to foolishly advocate IRV, but instead would be advised to 
> advocate RANGE VOTING (which experimentally favors all third parties
> far more than either plurality or approval, incidentally,
> see the CRV web site).
> -wds

-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
            Do to no one what you would not want done to you.
                  If you want peace, work for justice.