[EM] Ranked Preferences

[Juho]

I made a copy paste error.
> A will be eliminated. B wins.
should be
"L will be eliminated. R wins."

Juho

On Nov 17, 2006, at 18:58 , Juho wrote:

> Earlier I mentioned that the Ranked Preferences Method may need some
> fine tuning to avoid situation where votes of some voters may work
> against their interests. Now I found the time to do that.
>
> The Ranked Preferences Method could be characterized by saying that
> during the process of eliminating the candidates the votes are
> treated at each round in a way that we suppose to be in the best
> interest of the voters (no such strategic changes though that would
> depend on the progress of the calculation). This means that
> situations where the vote works against the voter's interests should
> be eliminated - also to avoid generating any need to change the
> sincere vote to a strategic one.
>
> I'll explain the new variant of the method starting from how the
> individual votes are handled. Capital letters indicate candidates
> that are still in the race.
>
> Vote a>>>B>c>>D>>e>F will be handled at this round (A, C and E have
> already been eliminated) as if it was a=B=c>D>e=F since >> is the
> highest preference relation that still has non-eliminated candidates
> at both sides.
>
> Relation >>> will be handled as = since after A has been eliminated B
> and C are now her favourites and she has no interest to push them
> down. This feature was not included in my previous description of the
> method.
>
> In addition to all this "dynamic interpretation" of the ranking based
> votes the method also has the tied at top and tied at bottom rules.
> Tied at top candidates are all considered to win each others but
> never lose to each others (+1 point in all comparisons). Tied at
> bottom candidates all lose to each others and never win each others
> (-1 point in all comparisons). (These rules are included to eliminate
> the need to put the top and bottom candidates in some preference
> order for strategic reasons.)
>
> Note that votes that use only one preference strength are calculated
> just like in the regular Condorcet methods. Tied at top/bottom rules
> however apply if = is used in addition to >.
>
> At each round each vote is thus processed so that first the strongest
> preference relation with non-eliminated candidates at both sides is
> sought. Then all other preference relations (than preferences of this
> strength that have non-eliminated candidates at both sides) are
> considered to be =. After this the matrix is calculated as usual in
> the Condorcet methods except that also tied at top and tied at bottom
> rules apply. Also the already eliminated candidates are included when
> counting the comparison results (remaining candidates may thus be
> beaten by them).
>
> After this the described method uses simply minmax(margins) to
> eliminate the weakest non-eliminated candidate. And sequentially
> drops candidates one after another until only the winner is left
> (dropping weakest groups would be an option, but a complex one with
> no very clear benefits).
>
> The result of the following example changes as a result of the
> changed rules.
>
> 45: L>>C>R
> 20: C>>R>L
> 35: R>>C>L
>
> I use * to mark the use of the tied at top/bottom rules.
>
> L-C = +45 -20 -35* = -10
> L-R = +45 -20* -35 = -10
> C-L = -45 +20 -35* = -60
> C-R = -45* +20 -35 = -60
> R-L = -45 -20* +35 = -30
> R-C = -45* -20 +35 = -30
>
> C will be eliminated. C would be the Condorcet winner in regular
> Condorcet elections where preference strengths are not taken into
> account. Top strength of the 20 C supporter votes is now ">".
>
> L-C = +45 -20 -35* = -10
> L-R = +45 -20 -35 = -10
> R-L = -45 +20 +35 = +10
> R-C = -45* +20* +35 = +10 (this value changed in the new variant)
>
> A will be eliminated. B wins.
>
> Juho Laatu
>
>
>
> P.S.
> In my first description from October 24th two lines should be changed
> to get this new version.
> - Add one point if x is ranked higher than y (top strength or higher)
> and
> - Subtract one point if x is ranked lower than y (top strength or
> higher)
> become
> - Add one point if x is ranked higher than y (top strength
> preferences with non-eliminated candidates at both sides)
> and
> - Subtract one point if x is ranked lower than y (top strength
> preferences with non-eliminated candidates at both sides)
> (Higher strengths need not be mentioned in the new version.)
>
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