[EM] generalization of AERLO/ATLO: S/WPO
jarmyta at antioch-college.edu
Sat Mar 19 21:40:09 PST 2005
AERLO and ATLO are anti-strategy enhancements proposed by Mike Ossipoff.
AERLO (automatic equal ranking line option) allows a voter to specify
that all preferences between candidates ranked above a certain line should
be changed to equalities in the event of an (all-majority-beats) majority
ATLO (automatic truncation line option) allows a voter to specify that
all preferences between candidates ranked below a certain line should be
changed to equalities in the event of an (all-majority-beats) majority
For example, lets say that my preference ranking is A>B>C>D>E>F>G>H>I>J.
I can vote A>B>C>(ERL)>D>E>F>G>(TL)>H>I>J, so that my ballot will be
changed to A=B=C>D>E>F>G>H=I=J in the event of a cycle.
However, what if (for whatever reason), I wanted my post-cyclic vote to
be A>B=C=D>E>F>G=H=I>J? AERLO/ATLO doesn't provide for this.
However, it is easy to generalize AERLO/ATLO into a system where voters
can specify precisely which preferences they would like to be changed to
equalities in the event of a cycle. Let's say that >> symbolizes a
preference that one doesn't want to be changed to an equality in the event
of a cycle (a "strong" preference), and > symbolizes a preference that one
does want to be changed to an equality in the event of a cycle (a "weak"
Thus, I could vote
A>B>C>>D>>E>>F>>G>>H>I>J to get
A=B=C>D>E>F>G>H=I=J in the event of a cycle
and I could vote
A>>B>C>D>>E>>F>>G>H>I>>J to get
A>B=C=D>E>F>G=H=I>J in the event of a cycle
For lack of a better title, I'll name this method strong/weak preference
I see two subtly different possible ways to count weak preferences:
(1) The direction of pairwise defeats are determined by both strong and
weak preferences, and the strength of pairwise defeats are determined only
by strong preferences.
(2) If there is a cycle, ballots are simply changed so that >> becomes >,
and > becomes =, and then an ordinary winning votes tally proceeds from
The difference in alternative (2) is that the direction of defeats can be
changed depending whether some preferences are weak rather than strong. I
suspect that alternative (1) will do better with the various
"continuity"-type criteria (like monotonicity), and so I provisionally
prefer (1) to (2).
Alternative (1) seems to be roughly identical to a proposal by Jobst on
9/6/04, which in turn was somewhat similar in spirit to a proposal of mine
on 6/19/04. It's quite possible that it has been proposed previously
without my knowledge.
Jobst September 6 2004:
James June 19 2004:
In technical terms, S/WPO methods have no disadvantages over AERLO/ATLO
methods, and they have a slight advantage in terms of flexibility. In
practical terms, S/WPO may or may not have a less intuitive ballot
I don't intend to imply that S/WPO is the best Condorcet anti-strategy
measure for public elections. I still claim that cardinal pairwise
deserves that distinction. I define S/WPO simply to add it to the list of
possible anti-strategy measures.
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