[EM] Truncation snapshot

[Elisabeth Varin/Stephane Rouillon]

Bart wrote:

>  How about the following:
>
> (projected vote percentages shown; assumed accurate to within +/- 5
> percentage points)
>
> 45%   A  B  C
>  5%   B  A  C
>  5%   B  C  A
> 45%   C  B  A

> Adam Tarr wrote:
> > Specifically, there is the remarkable fact that a voter in a winning
>
> > votes-based Condorcet voting system can NEVER be hurt by fully
> expressing
> > their preferences.  There are cases where fully voting your
> preferences can
> > fail to help you, but it can never actually hurt you.
>
> Never is a strong word.

To Bart:

This was the origin of the mail explosion.
I think truncation CAN hurt a Condorcet voting system using winning
votes
WHEN THERE IS NO CONDORCET WINNER.
Your example has one (B).
B 55 > A 45 and B 55 > C 45.
Search somewhere else.
Sorry, I though too you had it right
the first time.
I will think over to the question:
"Should we consider multiple truncation?"
My actual opinion is:
Yes, but maybe it has a lesser probability of occurence.

To Adam:

I agree mostly with your following analysis.
Technically, you should consider too the tie case.
It is improbable but possible.
But if your goal is to show that there is NO case
where truncation could hurt the result from the truncator
point of view and using wv, the tie case has to be treated.

Adam wrote:

> True, and I lack a rigorous proof, but every empirical example I have
> seen supports this.  Your example is no different...
>
>
> There's no sense in talking about uncertainty and ties; it only
> confuses the issue.  Let's just assume one or the other camp has more
> votes, and see if in that light, either side has an incentive to
> truncate.  If neither side has such an incentive, then neither side
> has that incentive in the toss-up case as well (since they know they
> either have more votes or less votes than the other guy).  Without
> loss of generality, I'll give A the edge, which gives us:
>
> 46 ABC
> 5 BAC
> 5 BCA
> 44 CBA
>
> Pairwise votes are:
>
> B 56 > C 44
> B 54 > A 46
> A 51 > C 49
>
> In this case, B is the Condorcet winner.
>
> If both sides truncate we get
>
> 46 A
> 5 BAC
> 5 BCA
> 44 C
>
> Pairwise votes are:
>
> A 51 > C 49
> A 46 > B 10
> C 44 > B 10
>
> Now A wins the election in either winning votes or margins (don't stop
> the presses yet).
>
> Now, if only the A camp truncates:
>
> 46 A
> 5 BAC
> 5 BCA
> 44 CBA
>
> Pairwise votes are:
>
> B 54 > A 46
> A 51 > C 49
> C 44 > B 10
>
> B wins the election in winning votes, and C wins the election in
> margins.
>
> Finally, if only the C camp truncates:
>
> 46 ABC
> 5 BAC
> 5 BCA
> 44 C
>
> Pairwise votes are:
>
> B 56 > C 44
> A 51 > C 49
> A 46 > B 10
>
> A wins the election in winning votes or in margins.
>
> OK, let's look at the decision matrix.  Here is the pairwise matrix of
> decisions for each camp, and the candidate elected, for each method:
>
> (I apologize in advance if the tables look lousy.  Try cutting and
> pasting into a text editor with uniform character spacing if it looks
> bad.  I used the "terminal" font type if that helps.)
>
> The top row is the tactics of the ABC faction, the left column is the
> tactics of the CBA faction.  T = truncate, NT = do not truncate.
>
> Margins methods:
>
>    | T | NT |
> ---|---|----|
> T  | A | A  |
> ---|---|----|
> NT | C | B  |
> -------------
>
> Winning Votes methods:
>
>    | T | NT |
> ---|---|----|
> T  | A | A  |
> ---|---|----|
> NT | B | B  |
> -------------
>
> OK, so what can we conclude from this?  If the CBA voters truncate,
> they always get A elected in either system.  This is a "strictly
> dominated strategy" to use the game theory name.  There's no way the B
> voters should truncate, regardless.
>
> In winning votes methods, truncation for the ABC voters makes no
> difference (i.e. does not hurt them, even if it fails to help them).
> In margins methods, truncating can prove costly for an ABC voter.
> This is neither here nor there for the purposes of my analysis; I can
> show you a counter-example where truncation can help in margins cases.
>
> The point is, nowhere here do we get any suggestion that a voter in a
> winning votes method can be helped by
> truncation.

To Adam, Alex, Mike and all winning votes partisans:

I agree on this. And thank you for showing it
for both winning votes and relative margins.
I will suppose only one side truncates even if it is not all clear to me
yet.
Let us measure the mean gain for those special case.
I will use a +1 gain for any winner ranking improvement, and a -1
for any winner ranking deterioration.
Winning votes for the ABC voters: mean impact: 0.
Winning votes for the CBA voters: mean impact: -1.
Typical impact of truncation using winning votes: -1/2.
Relative margins for the ABC voters: mean impact: -1.
Relative margins for the CBA voters: mean impact: -1.
Typical impact of truncation using winning votes: -1.
If you allow both truncation to occur you obtain the same
typical impacts, only the relative margins intermediates become -1/2 and
-3/2.

Of course this is only a sample analysis.
We should consider truncation from only a part of the group as a
possibility
and check if multiple truncations are equiprobable,
and finally count gain/deterioration one by one before averaging this.
I will soon start this analysis for small number of voters.

My actual problem was to determine what probabilities to use.
I came to this conclusion:
when one candidate outranks all the others,
he/she will win, margins or winning votes will
not make the difference. It is when the run is tight
between two, three or more candidates that the criteria
is important. But in this case pre-electoral information
is useless because, the error from polls has too much
incidence over the results. Thus, I will consider
any kind of ballot (truncated or not) possible with an equal
probability. When we do not know what to expect,
expecting any case with an equal weight seems the best approach to me.

>  But then I don't see truncation as necessarily a bad thing. If
> truncation can defeat a "hated middle" candidate, it addresses my main
> misgiving about the Condorcet methods.

> Much in the same way that we can't differentiate between the
> indifferent voter and the lazy voter, we cannot distinguish between
> the "respected (if unglamorous) compromise middle" and the "hated (yet
> still) compromise middle".  Smart CBA voters in an approval election
> will still approve B, to defeat A, anyway.  What method would actually
> prevent B from winning when the voters act in a logical manner?  Even
> plurality and IRV encourage CBA voters to dump C for B if they have
> perfect information.

To Adam:

See my previous mail, about methods to mix ranking methods
and Approval...

To Forest:

Thanks for reading about the universal ballot.
I like letters because it has not the grade/rank misunderstanding
possibility.
It can make easier to difference CandidateA = CandidateB from CandidateA
? CandidateB.
In the first case we can use the same letter for both candidates, and in
the second,
leave both unmarked.
However, I see no necessity against restricting the number of letter.
If there is 10 candidates, and if I do have a ranking for all of them,
please let me express it. It will not stop you from using only 2, 3, 5
or 7 levels
as you wish and still being compared fairly because the method is
pairwise comparison based.

To Matt:

Sorry but your error mail confused me a lot.
I do not think M. Ossipoff and Adam want to treat
unexpressed comparisons obtained by truncation as 1/2 votes.

To all:
I have a lot of fun and I am going to breakfast.

Steph.
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