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.la...@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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