[EM] Score DSV

[Jameson Quinn]

Good catch. Of course, this means that there must be more than 3 members of
the Smith set, as well as some other conditions (generally, of the voters
who consider A as neither worst nor best of the original Smith set, a larger
or "stronger" group must consider B as last than the group which considers B
as first; so this limits the number of voters who could see non-monotonic
results).

So you're right. Score DSV is only monotonic up to 3 (serious) candidates.
Make that 4 if you use the Dutta set (which cannot have 4 members) instead
of the Smith set. That is a better system generally except that it's more of
a pain to explain. Still, you've pointed to a clear advantage for Schulze.

So, how do you respond to the two things I see as clear advantages for Score
DSV over Schulze: the "defensive participation criterion" (*If a given
election chooses X, and new voters are added who prefer X over Y, then the
set of voters who prefer X over Y have some way of voting to make sure Y
does not win without reversing any preferences or falsely voting any
candidates equally.)* and the "ultra-strong defensive criterion"
(*non-dishonest
defensive strategies are always available to larger and/or more-motivated
groups (where motivation is counted relative to the Smith set) than the
corresponding offensive strategies*).

2009/8/29 Markus Schulze <markus.schulze at alumni.tu-berlin.de>

> Hallo,
>
> it seems to me that Score DSV does not satisfy
> monotonicity. It seems to me that the following
> scenario is possible:
>
>   Candidate A is the original winner.
>
>   Suppose some voters rank candidate A higher
>   without changing the order in which they
>   rank the other candidates relatively to
>   each other. Then it is possible that some
>   other candidate B is kicked out of the Smith
>   set and that, after renormalizing the ballots,
>   candidate A is worse off.
>
> Markus Schulze
>
>
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>
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