[EM] 28 years of progress and a wakeup call

[Closed Limelike Curves]

These are not strategically-viable ballots under Score (they don’t min-max).

On Tue, May 21, 2024 at 1:49 PM robert bristow-johnson <
rbj at audioimagination.com> wrote:

>
>
> > On 05/21/2024 4:38 PM EDT Closed Limelike Curves <
> closed.limelike.curves at gmail.com> wrote:
> >
> >
> > > I'm sorry. This "proof" cannot be true. It is certainly possible *not*
> to elect the Condorcet winner using either Approval or Score. This "proof"
> can be successfully refuted with a counter example. I posted one a few days
> ago regarding STAR (but it also says the same about Score and wouldn't be
> hard to modify to show that for Approval). A single counter-example is
> sufficient to disprove that conclusion that Approval and Score will
> (always) elect the Condorcet winner.
> >
> > Like I said, this holds true if voters are strategic. They pick an
> approval threshold between the frontrunners (more strictly, set it at the
> expected value of the election result).
> >
> > This is the minimal amount of strategy possible: just say you like a
> candidate if you think they’re above-average. I’m not aware of any system
> that requires less strategizing to get the same result, except *maybe*
> MDD//Score.
>
> I posted this here before, just last April.
>
>
>   L => Left candidate
>   C => Center candidate
>   R => Right candidate
>
> 100 voters:
>
>    - 34 Left supporters:
>    --- 23 ballots: L:5 C:1 R:0
>    ---  4 ballots: L:5 C:0 R:1
>    ---  7 ballots: L:5 C:0 R:0
>
>    - 29 Center supporters:
>    --- 15 ballots: L:1 C:5 R:0
>    ---  9 ballots: L:0 C:5 R:1
>    ---  5 ballots: L:0 C:5 R:0
>
>    - 37 Right supporters:
>    --- 17 ballots: L:0 C:1 R:5
>    ---  5 ballots: L:1 C:0 R:5
>    --- 15 ballots: L:0 C:0 R:5
>
> Now, in the STAR final runoff, the Center candidate will defeat either
> candidate on the Left or Right, head-to-head.
>
> Score totals:
>
>  Left   = 34x5 + 15 +  5  = 190
>  Center = 29x5 + 23 + 17  = 185
>  Right  = 37x5 +  9 +  4  = 198
>
> So who wins?
> With Score or FPTP, Right wins.
> With STAR or IRV, Left wins.
> With Condorcet, Center wins.
>
> Now, if you put the approval threshold somewhere between 1 and 5, then
> Approval comes out the same as FPTP.
>
> --
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
> .
> .
> .
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>
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