At 09:11 PM 5/11/2013, Jameson Quinn wrote:
What's with renaming later-no-harm as secret preferences? If you
want to make the argument that the name should be changed in
general, this one obscure web page seems to be a funny place to do
so. Sometimes it's worth just using the same words other people do.
Warren did add to the page that Secret Preferences was also known
as Later No Harm. I can readily understand why he did use a different
name. The name is horrible. It implies harm is done by voting
sincerely. Later-No-Harm implies that revealing a secret preference
harms someone. Whom?
The more-preferred candidate is alleged harmed by someone else
being elected. LNH-compliant methods *force* voters to keep lower
preferences secret, the method does not uncover them unless the
preferred candidate is eliminated. Note that this elimiination cuts
both ways. The secret preferences of other voters cannot save the
candidate from losing the election.
The implication is strong: compromise must only be allowed if the
first preference is *impossible*.
Therefore Later-No-Harm compliant methods are inimical to compromise,
and negotiating an optimal compromise is the principal mission of
voting system.
Along this line of thought, Approval fails LNH, because a voter who
votes a second preference as well as a first can cause the first
preference to tie, or, if a tie exists between the first and second
preferences, it can cause the second preference to win.
However, this is only visible if we know a secret preference. The
ballots won't show this.
Now, if the voter voted for A and B, which one did the voter harm? It
is true for either one that the other vote can cause the other to
win. In Approval, the situation is exactly balanced. Both votes
helped both candidates toward a win against all others. Essentially,
the voter has, if bullet voting, helped only one, and if voting for
two, has helped two *equally*. Only in the case that both candidates
are frontrunners is this problematic.
LNH failure, then, is only of interest to voters who might consider
approving both frontrunners. Where voters have a significant
preference, they will only approve one frontrunner, and not the
other. They have a *choice* of whether or not to approve both. We
must assume that if they do approve both, they have a weak preference
between them. The two votes then effectively expresses that weakness.
Approval is the first step into a world of methods that rank (or
rate) categories of candidates rather than candidates. It's up to the
voter what categories to place candidates in, and Arrow recently
explained in an interview that his famous Theorem did not apply to
methods like this.
Yet it is as simple as Counting All the Votes.
Essentially, LNH is a Criterion that can sound good on first contact.
It actively prevents a voting system from negotiating a fair
compromise, hence the Spoiler effect in Plurality and Center Squeeze
in IRV. It's simple to fix, but inevitably the fix causes LNH failure.
In highly polarized situations, voters will bullet vote and cause
Approval to default to Plurality. We can fix this either by using
IRV, with conditional lower ranked votes (i.e., all ranks allow
voting for more than one), but that method hasn't been well studied,
to my knowledge. It should work at least as well as IRV, though.
(With this, the voter chooses whether to vote approval style or IRV
style). And more complex methods can be designed. IRV probably
maximizes additional votes, but then proceeds to ignore many of them.
Bucklin appears, from history, to encourage substantial additional
approvals, in contested elections, possibly almost as many as does
IRV, because Bucklin offers conditional LNH protection. For unless
candidate is eliminated substitute candidate does not win with
higher ranked amalgamations.
Another approach to a fix can be done by using runoff voting, while
not reverting to Plurality in the first round. If the first round is
Bucklin, we can expect this system to somewhat depress the number of
lower ranked votes, because voters can defer that additional
approval decision even further than possibly by assigning a lower
Bucklin rank. (All Bucklin votes are approvals, merely conditional ones.)
If the runoff is also Bucklin, a voter could take an extended stand
for the favorite, waiting down through five simulated runoffs (if
it's three-rank Bucklin), before finally adding additional approvals.
There is a cost to this: the voter may then need to add additional
approvals, and may fail to get a more-preferred candidate into a runoff.
For a truly advanced system, I've suggested using a Range ballot in a
runoff system. The Range method must also indicate approval cutoff,
and that could be as simple as setting a certain rating as the
minimum approved rating. And Approved has a very specific meaning.
It doesn't meant that the voter has some absolute Approval
