[EM] An interesting example

Simmons, Forest simmonfo at up.edu
Thu Sep 22 12:52:57 PDT 2005

Here's an interesting example with four candidates, in which (under Shulze) an order reversal between Favorite and Compromise would give the win to Compromise (instead of a third candidate D) even though Compromise already beats Favorite.  In other words, there seems to be incentive to betray Favorite to help Compromise, even though Compromise already beats Favorite pairwise.
Of course there are many other opportunities for strategizing, and this favorite betrayal may not be the deciding factor in the end.  Another more conventional betrayal of F for A by 8 voters could over ride this F for C betrayal of 22 voters:
 8  FACD
 6  DCFA
100 total
D wins by Ranked Pairs, River, and Beatpath, whether margins or wv.
If  9 of the 22 FCAD voters betray F for C, then C wins under Beatpath, but not under River or Ranked Pairs.
If  19 of the 22 FCAD voters defect, then C also wins under River, but not under Ranked Pairs.
If all 8 of the FACD voters reverse F and A, then A wins under Beatpath, River, and Ranked Pairs no matter how many of the FCAD voters defect.
I'm sure that others will have additional insights into how truncations and equal ranking can affect the outcome.
It will be interesting to see the effect of various approval assumptions.
Note that even without any order reversals, C is the MinMax winner.
Since every candidate has a majority defeat, the MDDA winner will be the one with greatest approval, which is impossible to tell without additional information.
More analysis would be interesting.
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