[EM] Strategic voting in Condorcet & Range N-canddt elections - boiled down (& Ketchum reply)

[Dave Ketchum]

I said NOTHING about supposedly not caring about the current election,  
although, if the expectable winners seem equally distasteful to me I  
may not care as to that - assuming I do care, I should consider what  
would be the best strategy for that.

What I AM saying is that I may care about future elections, and need  
to consider what I can do now that will affect my future prospects.   
For example, the major parties could be agreed on topics such as  
abortion, marriage, or gun control, and a rising third party could, by  
rising fast enough, scare them into reconsidering (all without  
necessarily winning any election).

Dave Ketchum

On Jun 10, 2009, at 3:51 PM, Warren Smith wrote:

>> I would go for a different strategy - whatever leads toward long-term
>> strength.
>>
>> Winning the current election is usually pretty good.
>>
>> A third party, looking ahead, can think of what will make a stronger
>> future for it, even though perhaps not having a chance to win the
>> current election.
>
> --my strategy analysis was only about winning current election.  If  
> you do not
> care about current election, then it's a whole different ballgame.
> Still, if third parties always lose, then I don't see how they get
> long term strength!
>
> --Thinking some more about this whole argument, it can be boiled  
> down further.
> Here is the result:
>
> THEOREM:
> Consider a single-winner voting method that inputs rank-order ballots
> with rank-equalities permitted.  Assume the method is
> 1. monotone
> 2. always elects a candidate ranked unique-top by a majority (if+when
> one exists).
>
> [EXAMPLES of methods satisfying these conditions:
> Plurality, Black=Condorcet with Borda as fallback, Schulze beatpaths  
> Condorcet,
> Tideman ranked pairs Condorcet.   Where note Borda has to be defined
> in such a way it is monotonic even if equalities are permitted in
> rankings.
> Examples of methods NOT satisfying these conditions:
> IRV, Coombs, Nanson-Condorcet, WBS-IRV-Condorcet: not monotone.
> Borda: fails condition 2.]
>
> Fix the number N>=3 of candidates.
> Assume the number of voters is large and your vote is
> 1. unlikely to be capable of altering the winner
> 2. but if it can, it can only choose between TWO winners A & B;
> we assume elections in which your vote can choose between THREE OR  
> MORE
> winners are neglectibly unlikely.
>
> Then: a maximally-strategic vote for you (in hindsight, knowing all  
> ballots) is
> always of the form ranking A unique top, B unique bottom, and the rest
> in between in
> some manner (assuming you prefer A>B).
>
> Further, if everybody votes this strategic way, then A or B (one of
> the two "frontrunners") will always win except if there is a 3-way
> perfect tie (which we regard as neglectibly unlikely) and it will be
> the same winner as Plurality.
>
> COROLLARY 1:
> Under any circumstances where Approval is a better voting system than
> plurality for
> strategic voters, Approval also is a better voting system than every
> system meeting the criteria of the theorem (and with voters of the
> maximally-strategic ilk in the theorem).
>
> COROLLARY 2:
> Under any circumstances where Approval is a better voting system than
> plurality for
> strategic voters, and if "strategic range voters" mean the same  
> thing as
> "strategic approval voters", range is a better voting system than
> every system meeting the criteria of the theorem (and with voters of
> the maximally-strategic ilk in the theorem).
>
> REMARK 1:
> Range is known to be better than every rank-order ballot voting system
> for honest voters under the "RNEM" probability model, where "better"
> is measured by Bayesian Regret.  This proven by WD Smith in recent
> papers for each N=3,4,5,...,31.
> Permitting rank-order ballots to include equalities has no effect on
> this because in the RNEM exactly-equal utilities occur with
> probability=0, hence honest rank-order
> voters would not use them.
>
> So in these senses, range is better for both honest & strategic voters
> than every
> rank-order method meeting the criteria in the theorem, measured by
> Bayesian Regret.
>
> REMARK 2:
> Approval also is known to be better than or equal to every rank-order
> ballot voting system for honest voters under the "RNEM" probability
> model, where "better" is measured by Bayesian Regret, if N=3.
>
> REMARK 3:
> If N=4 and N=5 however, there exist rank-order systems superior to
> approval voting with
> honest voters (under RNEM).   Indeed, Borda is thus-superior, and
> certain Condorcet methods also appear to do this job.
>
> -- 
> Warren D. Smith
> http://RangeVoting.org  <-- add your endorsement (by clicking
> "endorse" as 1st step)
> and
> math.temple.edu/~wds/homepage/works.html