[EM] Probability of losing a sincere Cond. Winner

[Elisabeth Varin/Stephane Rouillon]

Adam --

I have very well understood you define a strong CW as having
more than 50% votes against any other candidate.

I made more comparative study of both ideal scenarios....

With my scenario, I would need to track and convince 11% of the 18%
potential truncaters in order to steal the strongly supported CW with
(wv)
(more than half).

With your scenario, you would need to track and convince 47% of the 49%
potential truncaters in order to steal the poorly supported CW with (rm)

and 48% of the 49% potential truncaters (almost all of them) in order to

steal the poorly supported CW with (margins).

It modifies the odds of an unsincere truncation, don't you think so?

But it dazzled me: almost all of the potential truncaters needed to
steal a strongly supported CW. You are right he is strong!

But again it depends on the criteria: if we compare the strongness of
the CW to
its stealer opponent using the other criterias, it is reversed.
Your "strong" CW has only a sloppy 2% margin advance over its potential
stealer.
Other margins in the scenario are greater.
My "weak" CW has 10 points of advance before losing its winning votes
duel.
Others advance are the same.

Your "strong" CW can get stolen by removing a huge support he had
against a third
candidate. My "weak" CW can get defeated by removing some of the direct
support
he had over its potential stealer.
How would these scenarios behave when candidates and voters increase in
number?
I do not know yet.

But it seems poorly-supported and strongly supported CW is a relative
definition
that can depend on the criteria too...

Steph.

> Adam--
>
> I fully agree with your way of seeing things.
> It is only about a matter of proportion were we do not see things the
> same.
> I will use samples of what follows.
>
>> But if you shift the percentages
>> around a little, or reduce the degree of truncation a bit in the edge
>> factions, then it breaks down.  Truncation only works strategically in
>> winning votes when there is a lot of truncation (indifference) to start,
>> and even then it only works in specific cases with fractured electorates,
>> where the Condorcet winner has pretty poor support from other factions.
>>
> With 3 candidates, I have to agree with you, even if I haven't yet
> done the calculus... It seems
> easier to build cases against margins than against winning votes. I do
> not know for relative
> margins...
>
> For more candidates, I do not know. But I think we have a problem of
> reference.
> You seem to be interested into american presidential election, with
> typically a small
> number of candidates (3 non-negligeable last time). I like it, but an
> electoral system
> should work well when multiple candidates run for office. Usually I
> think the more
> alternative a voter is offered, the more different debates and
> positions are offered
> and the healthier the democracy (if this does not paralyse the system
> by vote-splitting).
> French got 17 official candidates last time. If I remember well, 15
> were non-negligeable
> (it means by rallying their vote to the third runner, they could have
> changed the outcome
> of the election). In such a case, with 17 candidates, please do not
> tell me that truncation
> from start (sincer preferences) would not be the natural way to
> vote... (less than 60% of
> voters go vote already, and we only ask them to pick one name!)
>
> I admit my sincere Condorcet Winner has a "poor support" (thanks for
> answering with a good
> example for what I asked Mike) compared to your sincere Condorcet
> Winner.
> But what is more realistic? Identifying and convincing 18% of the
> voters to tilt their preferences
> from poll predictions as in my case, or 49% in your case. As you said
> my case is very unstable,
> I bet I would convince nobody. But what about yours? Even if I admit
> it is very more probable
> than mine, how probable is it? 1% of the cases? We definitively need
> to compute this number,
> even for the not so simple 3 candidates case with a small number of
> voters. Compared to the polls
> precision of 9 different ballots (A, B, C, ABC, ACB, BAC, BCA, CAB ,
> CBA) I think you would still
> convince nobody. Finally, with 4 candidates or more, forget polls
> precision, forget identifying voters
> with the same rankings, forget strategy at all. It has no mathematical
> relevance. It is too small cases.
>
> Since sincere preferences seem the most probable input, I think we
> should consider an equal probability
> of the 9 different ballots. I hope we can create a stealing CW case
> with few voters, because only with
> 4 voters we have 6561 equiprobable simulation cases...
>
> The next thing we will have to do is look at what happens when the
> number of candidates or/and voters
> inceases. Would the ratio (CW can be stolen cases / voting
> simulations) increase or diminish in each case?
>
>> This will be true in a huge range of cases -
>> basically, any time the second-place candidate's support for the winner
>> allows the winner to beat another edge candidate.  You can fudge the
>> numbers in the above example around a large amount and get the same results
>> - provided you don't give the George faction an absolute majority of course.
>>
>
> To summarize, I believe your "huge range of cases" will be incredibly
> small compared to the overall range of possibilities...
> And polls will not be sufficient to make it trustable enough, unless
> they can garantee less than 5 % errors and their result is your
> example.
> With your ideal example for winning votes a 6% error per kind of
> ballot could twist the result against truncaters wishes:
>
> 43%: George>Al>Ralph
> 6%: Al>George>Ralph
> 18%: Al>Ralph>George
> 33%: Ralph>Al>George
>
> So in your ideal case, yes you could convince some people. But even
> then, after looking at the real numbers, in most of the cases it would
> not change the outcome... (George would have won and still does, or Al
> would have won and still does) after polls errors corrections.
> I do not think preventing unsincere truncation should be the main
> issue. To me, optimal fairness of the representation of the wish of
> the people should.
> Unsincere truncation will almost never happen. Sincere truncation will
> almost always happen.
>
> Steph.
>
> Adam Tarr a écrit :
>
>> >This appears to be an example that illustrates a more stable
>> outcome is
>> >achievable
>> >by counting equal ranked options 1/2 vote each.
>>
>> Matt, we went over this before.  By adding 1/2 of a vote for each
>> side, you
>> turn winning votes into margins.  It's not a compromise in-between
>> the two
>> at all - it becomes margins exactly.  Adding half-votes in margins
>> does not
>> change the outcome at all.  So since Stephane cooked up his example
>> specifically to show when winning-votes encourages truncation (and
>> margins
>> does not) it's not surprising that adding half-votes "solves" the
>> problem.
>>
>> The reality, though, is that it's significantly easier to come up
>> with
>> examples where truncation is encouraged in margins-based methods.
>> Here's
>> the example Stephane came up with, casted into percentages and given
>> some
>> familiar names:
>>
>> 36% George
>> 9% Al>George>Ralph
>> 18% Al>Ralph>George
>> 18% Ralph>Al>George
>> 19% Ralph
>>
>> Ralph is the Condorcet winner, but truncation by the middle 18%, in
>> winning
>> votes, will give the election to Al.  But if you shift the
>> percentages
>> around a little, or reduce the degree of truncation a bit in the
>> edge
>> factions, then it breaks down.  Truncation only works strategically
>> in
>> winning votes when there is a lot of truncation (indifference) to
>> start,
>> and even then it only works in specific cases with fractured
>> electorates,
>> where the Condorcet winner has pretty poor support from other
>> factions.
>>
>> Contrast that to this case, which is not hard to come up with at
>> all:
>>
>> 49%: George>Al>Ralph
>> 12%: Al>George>Ralph
>> 12%: Al>Ralph>George
>> 27%: Ralph>Al>George
>>
>> Al is the Condorcet winner.  Now, if the George voters truncate in
>> margins,
>> they win the election.  This will be true in a huge range of cases -
>>
>> basically, any time the second-place candidate's support for the
>> winner
>> allows the winner to beat another edge candidate.  You can fudge the
>>
>> numbers in the above example around a large amount and get the same
>> results
>> - provided you don't give the George faction an absolute majority of
>> course.
>>
>> Winning votes gives the election to Al, even if George voters
>> truncate.  If
>> you add half-votes, then you run into the same problems you have
>> with
>> margins -- naturally, since adding half-votes turns winning votes
>> into margins.
>>
>> -Adam
>>
>> ----
>> For more information about this list (subscribe, unsubscribe, FAQ,
>> etc),
>> please see http://www.eskimo.com/~robla/em
>
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