[EM] 28 years of progress and a wakeup call

[robert bristow-johnson]

> 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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