[EM] Condorcet Cycle Observed in Minneapolis Election

[Colin Champion]

It's interesting that there was mandatory truncation in the election: 
voters were asked to rank "up to three candidates". That is something i 
hadn't considered in another thread.
    CJC

On 15/09/2022 12:05, Kristofer Munsterhjelm wrote:
> On 9/14/22 23:28, Andy Dienes wrote:
>> CVR available here 
>> https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/ 
>> <https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/> 
>>
>
> Looks right! Nice! I've attached the ballots in the more familiar EM 
> format.
>
> If we eliminate everybody but the Smith set, the ballots become:
>
> 1572: Arab
> 775: Arab>Gordon
> 133: Arab>Gordon>Worlobah
> 592: Arab>Worlobah
> 164: Arab>Worlobah>Gordon
> 822: Gordon
> 596: Gordon>Arab
> 205: Gordon>Arab>Worlobah
> 843: Gordon>Worlobah
> 334: Gordon>Worlobah>Arab
> 492: Worlobah
> 750: Worlobah>Arab
> 338: Worlobah>Arab>Gordon
> 852: Worlobah>Gordon
> 447: Worlobah>Gordon>Arab
>
> There's an Arab>Gordon>Worlobah>Arab cycle. Schulze and Minmax-type 
> methods elect Arab (whether restricted to the Smith set or not). 
> fpA-fpC restricted to the Smith set would give:
>
>     fpArab = 3236
>     fpGordon = 2800
>     fpWorlobah = 2879
>
>     score(Arab) = 3236 - 2879 = 357
>     score(Gordon) = 2800 - 3236 = -436
>     score(Worlobah) = 2879 - 2800 = 79
>
> and thus elect Arab. Smith//IRV would eliminate Gordon and then 
> Worlobah beats Arab pairwise.
>
> At least plain IRV chose a Smith set member here! But most of the 
> actual Condorcet methods prefer Arab.
>
> The first preferences before elimination are:
>     fpAnderson = 982
>     fpArab = 2719
>     fpGaskin = 546
>     fpGordon = 2508
>     fpUWI = 9
>     fpWorlobah = 2763
>
> So Friendly Cover would go: all Smith set members cover all the 
> non-Smith members, so everybody has {Anderson, Gaskin, UWI} as 
> friends, with a first preference sum of 1537. Then
>     Arab has himself as friend and Worlobah as defeater.
>         Score = 2719 + 1537 - 2763 = 1493
>     Gordon has himself as friend and Arab as defeater.
>         Score = 2508 + 1537 - 2719 = 1326
>     Worlobah has himself as friend and Gordon as defeater.
>         Score = 2763 + 1537 - 2508 = 1792,
>
> and Worlobah wins.
>
> So it agrees with Smith//IRV but not with itself restricted to the 
> Smith set, hence failing ISDA. I'm inclined to believe that Arab is 
> the right choice since so many other methods agree.
>
> -km
>
> ----
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