[EM] MAS defined.

Jameson Quinn jameson.quinn at gmail.com
Tue Oct 11 10:08:10 PDT 2016

 I've been thinking about default rules for MAS. Some desirable
characteristics for a default rule are:

-Should ensure that weak candidates don't win simply because all the
stronger candidates were eliminated.

-Should default to cooperation in a chicken dilemma with lazy voters.

-Should be summable.

-Should be easy to describe.

-Should make intuitive sense when described.

Here's the best I can do in terms of those criteria:

Each candidate's "expected downvotes" will be the number of upvotes for
candidates with a higher explicit score, minus half their explicit
midvotes. (This "half" could be any number between 0 and 1, under the
theory that some, but not all, of their explicit midvotes will come from
voters who upvoted candidates with a higher explicit score.) Their blank
votes will be counted as implicit downvotes until their total downvotes
reaches their expected downvotes; after that, blank votes will be counted
as implicit midvotes.

Almost-pathological scenario pair:


25: A(>B)

25: B(>A)

4: B>A

46: C(>>A,B)


25: A(>B)

29: B(>A)

10: C>A

36: C(>>A,B)

In scenario 1, A gets 44 implicit downvotes, thus 27 implicit midvotes.
Score is thus 2*25+4+27=81. B gets 46 implicit downvotes, thus 25 implicit
midvotes. Score is thus 30*2+25 = 85. B wins; correctly, I'd argue (B is

In scenario 2, A gets 41 implicit downvotes, thus 24 implicit midvotes.
Score is 2*25+24+10 = 84. B gets 46 implicit downvotes, thus 25 implicit
midvotes. Score is 2*29+25=83. A wins; again, this correctly found the CW.

Now, obviously, because this is working summably, there's no way for the
method to actually know whether the midvotes for A come from B voters (in
which case they don't change the CW from B) or from C voters (in which
case, they do). But I think that these scenarios are realistic in one
sense: if the C voters really do tend to prefer A over B, that will lead to
more explicit A midvotes than any realistic differential midvoting from the
A and B groups. Thus, while you could easily adjust either the above
scenarios to give the non-CW, I think that kind of result would be
relatively implausible.
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