Honest vs. manipulated ratings

[Saari]

In a message dated 98-05-07 12:31:05 EDT, you write:

> Ratings express more. However, 
>the two ratings will be equivalent unless the rates are intended to 
>express some strength of preference. In the latter case, the ratings 
>are more prone to manipulation than rankings.
>Ratings are for honest voters?

I think that the level of "prone to manipulation" depends on the method of
tallying as well as the method of voting, so the above claim is over-general.

For instance, assume a ranked ballot is tallied with the very-simple algorithm
"Count the first-place votes only - highest score wins."  This is equivalent
to the method used today in many places.  Under this system, information as to
the "likely frontrunners" will sway intelligent voters to cast a first-place
vote for one of several perceived frontrunners so as to ensure that their
opinion influences the outcome.  "Name recognition" campaigning is thus very
influential under this voting+tallying system.

Now assume a rated voting method of +10 to -10 on each candidate, and a simple
tally to generate the result.  Assume a given voter has a "complete list of
alternatives" and votes +10 on their top choice and -10 on their worst choice.
(This system doesn't really allow for expression of true "strength of
preference" on the top choice, but then neither does any ranked method which
always forces you to pick *somebody* to be first-choice.)

How should the voter vote on the remaining intermediate choices?

1) If there is not reliable info regarding the likely outcome, what to do?
Some people believe that casting a bunch of +10 and -10 votes is the most
rational, but I disagree.  If my second choice is "pretty good" then I believe
a +9.8 or +8 or some such vote is more intelligent than a full-strength +10
vote.  The precise value depends on the particular situation but it is the
principle I am concerned with here.  A +9 vote carries nearly as much weight
as the first-place +10 vote, AND it also contains some "tie-break" information
which gives some mild preference to my first choice over my second choice.
(The correct degree of preference is, again, dependent on the exact
situation.)

A quick illustration of this principle.  3 voters are choosing between 40
flavors of pie.  Each voter "likes" 20 flavors and "dislikes" the other 20
flavors, but the actual distribution is random.  Assume also that each voter
has some degrees of preference among the various "liked" and "disliked"
flavors.

IF each voter casts 20 "+10" votes and 20 "-10" votes, then on average 35
flavors will have been "vetoed" by one or more voters and the winner will be
chosen (presumably by lot) among the 5 flavors that received all +10 votes.
Any one of the five will be a decent outcome for this group - all five were
"liked" by all 3 voters and got a net score of +30.  (I also note that there
is no guarantee that a *ranked* voting/tallying method would necessarily
choose one of these five - the required data is not even present in the
ballots.)

Now for the same situation, suppose one of the three voters chooses instead to
spread out his/her votes, i.e. +10 for top choice, +9 for next, +8.9 for next,
+8.8 for next, etc. choosing some particular set of values as seems
appropriate.  Assume a similar spread between -5 and -10 for the "disliked"
choices.  What will be the outcome now?

The basic outcome is unchanged, i.e. 35 or so of the 40 choices were disliked
by at least one of the voters and gets a low score.  But the 5 "liked" choices
are now no longer tied.  One got +28.8 and won, the next got +28.6, the third
got +28.0, etc.

So by choosing NOT to exaggerate to a +10 vote on all liked choices, the
"honest" voter got a bonus - HIS preferences determined the final winner among
the 5 flavors which were all viable choices but otherwise tied.  In my view
this is a superior voting strategy.

Would the same principle apply if there were 30 voters?  I believe so - I
think the rationale is sound and equally valid regardless of the number of
voters.  I don't know how to prove this assertion...

I conclude that "honesty" is not a necessary requirement - that the most
greedy and selfish voter (if intelligent) must still conclude that an "honest"
vote is better.  Other voters may well choose to disregard this advice and
vote all +10's and -10's and that is their choice.  But I believe they are not
being as effective as they could if they do so.

2) IF there is some widespread preknowledge of the "likely outcome", then this
raises a strong incentive to "vote tactically", i.e. artificially elevate an
otherwise honest +8.8 vote to +10, or downgrade an otherwise honest -3 vote to
-10.  However, I again conclude that this strategy, though tempting, is
ultimately counterproductive.

My rationale: The only reason to do such a tactical vote is to try to change
the outcome. Assume that some (presumably intelligent) voters do just that.
The result may change, and I as a voter can no longer assume that I have an
accurate prediction of the "likely outcome".  But without an accurate
preassessment, a tactical vote can easily backfire.  My altered vote might
result in a poorer result not a better one.  Should I take the chance, given
that the supposedly accurate advance prediction really isn't?

This is only a sketch of the logic, but it shows why I conclude that even with
preknowledge of the "likely outcome" I am really better off to simply vote
honestly.  It has nothing to do with honesty or values per se, just rational
thinking and trying to cast the most useful (by my standards) vote that I can.

The bottom line: Rated vote methods may not be as vulnerable to exaggeration
as is often implied.

Mike Saari