VA, Margins, & voter wishes -- the 1/2 vote option

Hugh R. Tobin htobin at
Sun Oct 4 12:45:40 PDT 1998

The logigal middle ground between Votes-Against (VA) and Margins (as the
tiebreak in Smith//Condorcet or similar system) is to modify VA by
allowing each voter to choose, with respect to each equal ranking of X
and Y on his ballot (including implicit equal rankings of candidates
left off the bottom), whether it should count as 1/2 for each, or zero
for each, in the pairwise race X vs. Y.  If all voters choose the 1/2
option in each case, then we have the equivalent of margins.  However, a
voter with the preference profile A=B>C would not rationally choose the
1/2 option, because it dilutes the effect of the vote against C.  That
is, if the cycle is C>A>B>C, then C might win a circular tie by being
less beaten than A and B if the A=B>C voters were to select the 1/2
option, when C would lose the tiebreak to B if those voters were to
select the zero option.  This is essentially the point Markus makes on
the attractiveness of upward truncation in VA. Given the zero option,
voters might be induced to suppress (mild) true preferences at the tops
of their ballots in order to maximize the power of their votes against
the greater evil, but that is not necessarily an objection to a system
allowing maximum voter choice.

The default option on the ballot, to reflect the presumed intent of the
voters, would be "zero" for equal rankings at the top and "1/2" for
equal rankings at the bottom.  Absent express selection by the voter,
A=B>C>D=E would translate into:

1 A>C
1 A>D
1 A>E
1 B>C
1 B>D
1 B>E
1 C>D
1 C>E
1/2 D>E
1/2 E>D

 (obviously some default rule would be needed for equal rankings in the
middle as well). 

In the VA [1/2 option] system, random selection strategies would not be
needed in order to exercise one's full voting power in favor of a
candidate. But if Mike O. believes it is sometimes rational to choose
"zero" when voting A>B=C, as part of a scorched-earth
anti-order-reversal strategy, he can do so by checking the appropriate
box on the ballot.

Does this compromise please everybody? :>)  Is there any reason why it
should not be used with beat-paths, or why the appropriate default
option would be different?

-- Hugh Tobin

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