[EM] 28 years of progress and a wakeup call

[Closed Limelike Curves]

>if you put the approval threshold between 1 and 5

Yes, so voters would not pick that approval threshold in strategic
equilibrium. Myerson and Weber calculate the approval threshold strategic
voters will use, and find it elects the Condorcet winner.

On Tue, May 21, 2024 at 1:51 PM Closed Limelike Curves <
closed.limelike.curves at gmail.com> wrote:

> 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."
>>
>> .
>> .
>> .
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20240521/5e803b5d/attachment.htm>