[EM] Condorcet question - why not bullet vote

[Juho Laatu]

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?

> - 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?

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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