Anonymous user
D2MAC: Difference between revisions
no edit summary
imported>Heitzig-j |
imported>Homunq No edit summary |
||
| (2 intermediate revisions by one other user not shown) | |||
Line 26:
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).
''This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.''
===Two factions with a compromise option and unilateral cooperation===
Line 44:
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.
''This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of
===Two factions with a compromise option and bilateral partial cooperation===
Line 92:
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
==Variants==
Line 117:
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.
[[Category:Single-winner voting
| |||