[EM] Ranked-ballots and strategic voting (Was - truncation in IRV example (as requested by Benham))

[Paul Kislanko]

Warren's example for IRV provides an excellent description of why I prefer
ranked-ballots with equal-rankings and truncation allowed, and prompted
these comments.

Note that in the example forcing the last 3 voters to list all preferences
caused their LEAST favorite to win. This is a nice demonstration of what I
meant the other day when I suggested that as a voter I fear "bad things will
happen" if I'm required to list a candidate I definitely do not want under
any circumstances.

>From the voter's perspective it bothers me that in order to prevent my
least-desirable alternative from winning I need to know:

1) in detail how the vote-counting method works
2) EXACTLY how all other blocs of voters will vote

and only if I have that information - incredibly unlikely in the general
case - can I apply the appropriate "strategy" to elect one of my favorites.

Philosophically, I do not think the voters should have to understand
combinatorics to be allowed to vote. But I think much of the "strategy
flaws" in methods (there must always be some) can be ameliorated by
separating the preference-collection analysis from the counting-votes
analysis.

In any ranked-ballot method (for either single or multiple -winner
elections) as if the voter is really choosing EXACTLY ONE from among the
choices of possible ranked-ballots. The voter, of course, doesn't realize
that as she ranks 1st, 2nd etc. but logically that is what happens, which is
why we display the preferences in tables as we do.

Side note: in Warren's example, there are more possible choices than there
are voters, since there's 21 voters and 24 possible orderings of 4
candidates. That's irrelevant to the example, but it gets to heart of the
matter. For the failure to be demonstable, and a "strategy" to be available,
83 percent of the possible choices had to have no voters select them.

In theory, pollsters could give their sample voters a list of all 24 choices
and ask them to pick one, and thereby provide enough information to the
electorate to decide how best to alter their choice to minimize the chances
of a "bad outcome", but since all voters who know how the counting method
works will do this, the poll results are invalidated, and you're into the
game-theoretical part "if the polls are right I should falsely vote for
ranking 23 instead of ranking 16, but if the A voters all switch to ranking
13 I'd be better off with ranking 15..." and everybody's more worried about
other voters than candidates or issues and EVERYBODY votes falsely.

But if you allow equal rankings and truncations, I don't have to worry that
my ballot which DOES NOT list A will cause A to get elected, and all I have
to think about is which candidates come closest to my preferences for issues
based upon importance of issues and number of issues for which the candidate
matches my choice.

And I'm less worried about other voters "stealing" the election by
exploiting available strategies. If equal rankings and truncation are
allowed, with 4 alternatives there are 79 different possible rankings, not
just 24. The voter's job is no more difficult - in fact it is much easier
than ranking all 4 alternatives - but now gathering enough information to
apply a strategy based upon false preferences is nearly equivalent to
holding the election. 

The pollsters can still ask the same question - Which of these 79 choices is
most nearly how you think you'll vote? is not likely to be answered the same
way twice by anybody. 

> -----Original Message-----
> From: election-methods-bounces at electorama.com 
> [mailto:election-methods-bounces at electorama.com] On Behalf Of 
> Warren Smith
> Sent: Tuesday, October 18, 2005 2:31 PM
> To: election-methods at electorama.com
> Subject: [EM] truncation in IRV example (as requested by Benham)
> 
> example of situation in IRV where truncating a ballot
> is strategically desirable:
> 
> If your favorite is F but F is eliminated in round 1,
> and the rest of your ballot is a "no show paradox" example
> in which you are better off "not showing up to vote",
> then truncating your ballot
>   F --the rest truncated---
> is strategically superior to voting
>   F honest-ranking-of-others.
> 
> So it is merely a matter of producing no-show-paradox examples
> for IRV (or any other such voting system).  Many are known...
> 
> Explicit example From an old EM post by me (note 2) and
> [SJ Brams: Voting procedures, ch. 30 pp.1050-1090 in
> vol 2 Handbook of Game theory, ed. R.Aumann and S.Hart,
> Elsevier Science, NY 1992]
> 
>  A>B>C>D  7 votes
>  B>A>C>D  6
>  C>B>A>D  5
>  D>C>B>A  3
> IRV ==> A wins.  (Elim order: D, B, C.)
> 1. This is despite fact B is Condorcet winner, i.e. would win direct
> pairwise elections versus every opponent!
> 2. If the 3 voters in the last row instead had
> ranked D first - but refused to say more, i.e. refused to provide
> their 2nd 3rd 4th choices -
> then B would have won (which those voters prefer over A).
> This illustrates the fact that in IRV, voters can be motivated to
> refuse to rank-order some of the candidates, thus defeating 
> IRV's purpose
> of garnering ordering information from the voters.
> 3. And: if these 3 voters instead had dishonestly voted
> A>D>C>B  then B would have won (which they'd prefer to A)
> despite fact they just RAISED their opinion of A to
> first place and nothing else changed! That is
> an example of "non-monotonicity".
> 
> wds
> ----
> election-methods mailing list - see http://electorama.com/em 
> for list info
>