[EM] Condorcet Cycle Observed in Minneapolis Election

Kristofer Munsterhjelm km_elmet at t-online.de
Thu Sep 15 04:05:57 PDT 2022


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
-------------- next part --------------
334: Gordon>Worlobah>Arab
351: Arab>Anderson
257: Arab>Anderson>Gordon
795: Arab
586: Gordon>Worlobah
196: Arab>Anderson>Worlobah
633: Worlobah>Gordon
208: Gordon>Arab
130: Gordon>Worlobah>Anderson
290: Gaskin
253: Worlobah>Arab
338: Worlobah>Arab>Gordon
404: Worlobah
483: Gordon
205: Anderson>Arab
258: Arab>Gordon
63: Anderson>Gordon>Arab
129: Arab>Gordon>Anderson
78: Anderson>Arab>Worlobah
36: Gaskin>Anderson>Arab
188: Gordon>Arab>Anderson
133: Arab>Gordon>Worlobah
37: Arab>Anderson>Gaskin
16: Gaskin>Arab>Anderson
43: Gaskin>Gordon>Anderson
205: Gordon>Arab>Worlobah
80: Gordon>Anderson
355: Worlobah>Arab>Anderson
200: Arab>Worlobah>Anderson
120: Gordon>Anderson>Arab
229: Anderson
3: Worlobah>Gaskin
56: Anderson>Gordon
78: Gordon>Anderson>Worlobah
29: Worlobah>Anderson
130: Worlobah>Gordon>Anderson
22: Anderson>Worlobah
86: Worlobah>Anderson>Arab
40: Anderson>Worlobah>Arab
106: Anderson>Arab>Gordon
6: Anderson>Arab>UWI
107: Arab>Worlobah
4: UWI>UWI>UWI
5: Worlobah>Gordon>Gaskin
447: Worlobah>Gordon>Arab
164: Arab>Worlobah>Gordon
26: Gordon>Anderson>Gaskin
4: Gordon>Gaskin>Arab
2: Gordon>Arab>UWI
30: Anderson>Arab>Gaskin
45: Worlobah>Anderson>Gordon
19: Anderson>Gaskin>Gordon
34: Anderson>Gaskin
29: Arab>Gaskin
5: Arab>Worlobah>Gaskin
3: Anderson>Gordon>Anderson
38: Gaskin>Gordon
4: Arab>Gordon>UWI
6: Anderson>Worlobah>Gaskin
9: Gordon>Worlobah>UWI
30: Gaskin>Anderson
22: Gaskin>Anderson>Gordon
22: Anderson>Worlobah>Gordon
15: Gordon>Gaskin
30: Anderson>Gordon>Worlobah
4: Arab>Anderson>UWI
19: Arab>Gaskin>Anderson
2: Gaskin>Gordon>Worlobah
3: Arab>Anderson>Arab
2: Gaskin>Worlobah>Anderson
3: Worlobah>Anderson>Gaskin
13: Anderson>Gaskin>Arab
9: Worlobah>Gordon>UWI
8: Gordon>Arab>Gaskin
1: Worlobah>Gaskin>UWI
17: Gordon>Gaskin>Anderson
7: Gaskin>Arab>Gordon
16: Gaskin>Arab
4: Arab>Gaskin>Gordon
1: Gordon>Arab>Gordon
4: Worlobah>Arab>Gaskin
4: Anderson>Gaskin>Worlobah
5: Gordon>Gaskin>UWI
3: Gaskin>Gordon>UWI
2: Gaskin>Gordon>Gaskin
2: Worlobah>Arab>UWI
2: UWI
4: Worlobah>Gaskin>Gordon
2: Gaskin>Gordon>Arab
1: Gordon>UWI>Worlobah
10: Gaskin>Anderson>Worlobah
1: Gaskin>Worlobah
3: Arab>UWI>UWI
3: Anderson>Worlobah>Anderson
3: Gaskin>Anderson>UWI
9: Arab>Gordon>Gaskin
1: Arab>Gaskin>Arab
1: Gaskin>Gaskin
10: Gaskin>UWI>UWI
2: Gaskin>Arab>Gaskin
2: Anderson>UWI>UWI
8: Anderson>Gordon>Gaskin
3: Gaskin>Worlobah>Gordon
1: Arab>Gordon>Arab
2: Arab>UWI
1: UWI>Gaskin>Gordon
3: Gordon>Worlobah>Gaskin
2: Arab>Arab
5: Worlobah>Arab>Worlobah
2: Anderson>Gaskin>UWI
1: Gaskin>UWI>Anderson
2: Arab>Gaskin>UWI
3: Arab>Worlobah>Arab
1: Gaskin>UWI
1: UWI>Anderson
2: Worlobah>Gaskin>Arab
1: Worlobah>Anderson>UWI
2: Gaskin>Arab>Worlobah
1: UWI>Worlobah>Arab
4: Gordon>Gaskin>Worlobah
1: Gaskin>Anderson>Gaskin
1: Gordon>UWI
1: Worlobah>Worlobah
2: Worlobah>Gaskin>Anderson
2: Gaskin>Worlobah>Arab
1: Worlobah>UWI>Gordon
1: Anderson>UWI
1: Arab>Worlobah>UWI


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