D2MAC: Difference between revisions

===Two factions with a strong compromise option: strategic considerations===

Assume these voters have the following cardinal utility functions:

: 55 voters: A 100, C 80, B 0

: 45 voters: B 100, C 75, A 0

Then it is quite probable that voters will behave like this:

: first 55 voters: A favourite, C also approved.

: other 45 voters: B favourite, C also approved.

This is because this voting behaviour of "full cooperation" is a group strategic equilibrium, which means that no group of voters would wish to have voted differently. To see this, note that with the above behaviour, C is the certain winner and the expected utilities for the voters are

: first 55 voters: 80

: other 45 voters: 75

Had some ''x'' of the last 45 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 75, namely

: (''x'' % + (45 - ''x'')% * ''x'' %) * 100 + (100 - ''x'')% * (100 - ''x'')% * 75 = 75 - 0.05 ''x'' - 0.002 ''x'' ² < 75.

Analogously, had some x of the other 55 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 80.

Note that the resulting total (expected) utility is approx. 78. If A had been declared the winner (as majoritarian methods do), it had only been 55.

''This shows that D2MAC can be more efficient in maximing total utility than majoritarians methods.''