Problems with the majority requirement
On Fri, May 30, 2003 at 10:55:44AM -0400, Nathanael Nerode wrote:
> I'm not advocating getting rid of the majority requirement. A winning
> option should have to beat the default option, and this creates no
> serious voting problems that I can see.
I was with you until here. I think it creates very similar
problems. I'm going to summarize here, and then I'll try to let
this debate go except to clarify.
Specifically, I think there are three issues with the requirement
that an option defeat the default option head-to-head, in order to
qualify for the Condorcet round (I'm ignoring supermajorities and
quorums entirely).
The first two assume that voter preferences about the default option
are like preferences about any other. The third questions this
assumption, and is perhaps more than one issue (I'm not overly clear
on it myself). You can skip the third if it makes your head hurt
like mine. (However, if you disagree that voters can have
preferences about the default option just like any other, I guess
the third comes into play.)
I'll preface this by saying that this whole problem turns out to be
more subtle than I'd believed, even after having read and thought
about the stuff on electionmethods.org.
1. A voter who sincerely prefers the default over some other option
is in effect pursuing a "meta-strategy"--ie, one that is outside the
voting system per se. However, a voting system (such as the
proposed) that gives extra weight to the default option effectively
promotes this meta-strategy. I leave to others to decide on the
value or harm of this meta-strategy--if you think that there should
be an avenue for obstructionism, you probably don't see this as a
problem.
2. A voter who sincerely prefers some option over the default may
still have an incentive to vote the default higher. By weakening
the demoted option, he may cause his favorite to win. This is true
in straight Condorcet systems, but is more likely in the proposed
system, given the "knockout punch" of the default option. I
consider this a serious problem. I think I have given some
reasonably arguments and examples to support this, but I can try for
more if needed.[1]
3a. Due to the inherent meaning of the default option, voters will
typically not consider it especially undesirable (unless they
strongly feel that a revote will create tension or damage Debian's
reputation...). This inclines voters to insincerely promote the
default option, since causing the default to win is a small penalty.
Arguably, a voting system should counterbalance this inclination.
3b. One's feelings about the default option are inextricably tied
to the workings of the voting system (because you'd want to take
into account the possible outcomes of the next vote(s)). This makes
the problem quite circular. I frankly don't know how to resolve
that, and I don't sense that anyone really wants to. (You could try
to undercut this problem by artifically making the default option
less desirable. Eg, if there is a revote, anyone who voted for the
default option has to close 3 bugs if he wants to vote again. Or
use RedHat for a month.)
Andrew
[1] As an aside, there is a case that vexes me considerably, and it
pertains to pure Condorcet/CpSSD. Say you have sincere preferences
8 ABC A>B 8:7 A wins
7 BAC A>C 15:5
5 C B>C 15:5
If only A swaps B and C, the outcome is the same. If only B swaps A
and C, B wins in the tie-break (A>B 8:7, C>A 12:8, B>C 15:5). If
both swap, C wins outright. (There are of course more
possibilities, such as truncating and splitting up the votes among
sincere, swap, and truncate, but they don't seem to make any
difference.) So, A voters should vote sincerely, since that always
gives them the best outcome. Given this, B voters should swap,
since that gives them the best outcome when A votes sincerely. So,
B should win the election.
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