y/n strategic instability. 6-Candidate example.
dfb at bbs.cruzio.com
Fri Nov 15 22:43:38 PST 1996
I will reply to Demorep's 2 examples, his 6-candidate example, &
his 7-candidate example, as soon as I reply to Don's latest
garbage-dumping on ER.
But, briefly, about Demorep's earlier 6-candidate example:
Smith//Condorcet, the main recommendation of EM, doesn't
elect a candidate who has received "no" from a majority.
Has Demorep shown that plain Condorcet can elect a candidae
who isn't in the Smith set? Yes. We already knew that. And,
because of the possibility of criticisms based on examples
like this one, we recommended Smith//Condorcet, though it
seems to me that there's no really conclusive argument for
or against the use of the Smith filter.
But Demorep's 6-candidate doesn't fill the bill:
Demorep was asked to give an example where Condorcet
chose an alternative receiving "no" from a majority when
there were alternatives that didn't receive "no" from a
majority and which didn't have a pairwise majority against
them. Demorep hasn't done that, with that example, though
I hasten to admit that that example is an improvement over
Demorep's use of the Titanic as an example :-)
Ok, then let me be the one to give an example where not just
plain Condorcet, and not just Smith//Condorcet, but _any_
method will choose an alternative that has "no" from a majority,
when no other alternative has "no" from a majority, and where
no alternative has anothr alternative ranked over it by a majority.
(Of course when I say "any method" I mean any method that doesn't
take y/n votes)
Here's the example. No, this isn't a Don-like joke:
The "/" mark indicates that every alternative after it, or
unranked in that ranking receives a "no" from that voter.
A wins by any method. A is the only alternative receiving
"No" from a majority of the voters.
Of course such examples can be constructed: Rank balloting
method & y/n voting are 2 entirely different things. It would
be surprising if neither ever ran afowl of the other.
So if Demorep is intending to demonstrate that it's possible for
a method that doesn't use y/n voting to produce a winner that
y/n voting wouldn't allow, then that isn't really an astounding
People on EM who have commented on y/n voting haven't opposed it,
though there have been some misgivings that (to use some of
Demorep's cast of characters), Ghengis Khan, Hitler or Stalin
could take over if there were a vacuum of power due to
no one being elected, due to getting "No" votes from a majority.
Actually, that deoesn't seem a danger if we merely held another
election as soon as possible. It would be the old expense objection--
the cost of a 2nd election. It would be a matter of which is more
important to acceptance: The voters's cynicism or their avoidance
of expenditures. We've already said that polling & focus groups
will determine whether or not y/n voting would be a desirable
thing to add to a proposal, or whether it would add one change
too many, creating a bigger target, easier to shoot down. But
I don't know why Demorep is trying to convince us, sincve
those who have commented have said that it should be up to the
public, and not decided byk the electoral reformers.
By the way, in Demorep's 6-candidate example, using plain
Condorcet, and counting "/" as "no winner", the winner of the
election is "no winner".
Demorep exaggerates the need for y/n. Sure, I'd have used it
in the '96 elections, and we should have had it. But in
rank-balloting elections (as has been explained to Demorep
10^6 times) there'd be such good selection that everyone would
be able to vote for someone. My reason for wanting to have
NOTB in '96 is to vote against everyone, invalidating the
election. But if there were someone I could vote for, I wouldn't
In fact, y/n would be likely to be strategically unstable,
leading to a wholesale mutual massacre of candidates.
If we had y/n, regardless of the voting method, I'd of course
vote "No" on the Democrats & Republicans. If a number of others
would, then it would be quite obvious to Republocrats that they
could remove their big-party rival by voting "No", and creating
a "No" majority for hir.
In fact, for that reason, there'd be a "defensive" need
for Republocrat voters to vote "No" on their big-party Rival,
because if hir voters are going to use that strategy, then
one should prevent one's own candidate from being the only
one disqualified in that way. Maybe a Republocrat voter
could thereby turn a lone disqualification into an
invalidated election, thereby giving hir candidate another
chance in the next election.
So y/n voting seems to have strategic instability that would
be a problem.
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