[EM] Condorcet question - why not bullet vote

[Peter Zbornik]

On Thu, Jun 17, 2010 at 1:06 AM, Juho Laatu <juho.laatu at gmail.com> wrote:

> On Jun 16, 2010, at 11:49 PM, Peter Zbornik wrote:
>
> Juho,
>
> we have the example
> 49: A
> 48: B>C
> 3: C>B
>
> you wrote to me:
> "- C loses to B, 3-48. In winning votes the strength of this loss is 48.
> - B loses to A, 48-49. In winning votes the strength of this loss is 49.
> - A loses to C, 49-51. In winning votes the strength of this loss is 51."
>
> Thus: "If the three C voters will truncate then they will win instead of B
> in winning votes based Condorcet methods."
>
> This is correct, if proportional completion is not used (see page 42 in
> http://m-schulze.webhop.net/schulze2.pdf)
> If proportional completion is used (which I would recommend) then B wins.
>
>
> Yes, the example applies to (typical) winning votes based methods. Other
> approaches like margins and the referenced approach may provide different
> results.
>
>
> If proportional completion is used, then we need to fill in the preferences
> of the ones who did not vote:
> We have 100 voters.
> - C loses to B, 3-48, means 49 voters did not vote. We split each voter
> into two: the first has weight 3/51 of a vote and the second 48/51, which
> gives a total score of 49*3/51+3 vs 49*48/51+48
> - B loses to A, 48-49, means 3 voters did not vote. We split each voter
> into two: the first has weight 48/97 and the second 49/97, which gives a
> total score of 3*48/97+48 vs 3*49/97+49
> - A loses to C, 49-51, means all voters voted.
>
> Thus after the proportional completion, the vote tally is the following:
> - C loses to B, 5,88-94,12. In winning votes the strength of this loss
> is 94,12.
> - B loses to A, 49,48-50,52. In winning votes the strength of this loss
> is 50,52. (delete this link first)
>
>
> What link?
>
http://en.wikipedia.org/wiki/Schulze_method#The_Schwartz_set_heuristic,
point 3

>
> - A loses to C, 49-51. In winning votes the strength of this loss is 51.
>
> Thus B wins if proportional completion is used. C wins without proportional
> completion.
>
>
> There are many different approaches to measuring the preference strength of
> the pairwise comparisons. Winning votes and margins are the most common
> ones. The referenced approach would be a third approach. It seems to be the
> proportion of the given votes. Correct?
>
Yes, the proportion is the same and the result is scaled up to the number of
voters, and is suggested by Markus Schulze as mentioned below.
Something similar (splitting up observations into two complementary) is done
in statistics, when measuring the predictive strength of a logistic
regression function on validation data.

>
> 94,12 = 100/(3/48+1), i.e. the proportion of the preferences (48:3) scaled
> in another way (100/(1/x+1))
>
> (Shortly back to the original question. Unfortunately I don't have any
> interesting proportion specific truncation related examples or properties in
> my ind right now.)
>
> Juho
>
>
>
>
>
> Best regards
> Peter Zborník
>
> On Wed, Jun 16, 2010 at 9:35 PM, Juho <juho.laatu at gmail.com> wrote:
>
>> On Jun 16, 2010, at 9:39 PM, Peter Zbornik wrote:
>>
>>  In what situations will bullet voting help my candidate to win
>>> (considering the advanced Condorcet systems)?
>>>
>>
>> Here's one more example where a reasonably small number of strategic
>> voters can change the result.
>>
>> 49: A
>> 48: B>C
>> 3: C>B
>>
>> If the three C voters will truncate then they will win instead of B in
>> winning votes based Condorcet methods.
>>
>> Juho
>>
>>
>>
>>
>>
>>
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