[EM] [CES #8174] Criteria satisfied (and not) by score voting

[Abd ul-Rahman Lomax]

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 judgment 
of the candidate. It is a *choice,* only. The choice is this: does 
the voter prefer the candidate being elected to deferring the 
decision to lower ranks, or to a runoff, if it's the first election. 
That's an absolute preference, it's a comparison. Yes, it involves 
complex strategy if the voter wants to give it that much thought. 
Most voters won't do that, but their guesses will probably, on 
average and with experience, reflect something close to their real preferences.

With a Range ballot of sufficient resolution, many candidates could 
be ranked. If the number of ratings is equal to the number of ranks, 
an easy default rating is obvious: just rank them. This would then be 
a Borda ballot. However, it allows equal ranking and it allows 
skipped ranks. (Real Bucklin did both.) The difference between 
Bucklin, then, is that rating of unapproved candidates becomes 
possible. If a plurality decision is to be made, that's necessary for 
optimization, because it does matter. IRV allows the voter to vote in 
these "unpalatable" races. With sufficient Range resolution, the 
"harm" to the favorite is tiny, and in a primary, the only usage of 
lower preferences would be for pairwise analysis, to ensure that a 
Condorcet winner makes it into the runoff.

The runoff can have more than two candidates. If it's a Range ballot, 
the top two sum-of-votes candidates may go into the runoff, and if 
there is a candidate who beats them both, pairwise, that candidate 
can be there as well. The final ballot form? Bucklin would do very 
well and is very simple to vote. Range aficionados would want pure 
Range, and there is value to that. It could be Bucklin using a full 
Range ballot.

(Bucklin is essentially median Range; Bucklin satisfies the majority 
criterion and only fails where multiple majorities are involved, a 
technical point. In the primary, an obvious and simple standard for 
going to a runoff is majority approval. No majority approval, no 
runoff. However, there can be some other additional criteria: for 
maximized performance, simple multiple majorities could got to a 
runoff. (This demolishes the argument that Bucklin does not satisfy 
the Majority Criterion). Condorcet failure? Runoff.

(In reality, with sufficient resolution, multiple majorities would be 
rare in seriously contested elections. They did happen with Bucklin, 
on occasion.)

(To count a Range ballot as Bucklin, just start adding in votes in a 
simulated series of Approval eletions, starting with the top rating 
and moving down, until a majority is found or the ratings have been 
exhausted. In a first round Bucklin election, majority required, stop 
counting when a majority is found; if the necessary rating round to 
reach that is below the defined approval cutoff, the election fails. 
There would then be various ways of determining runoff candidates.)

Hybrid systems can satisfy all reasonable voting systems criteria. 
LNH, probably not. It intrinscially conflicts with Condorcet 
criterion, which is highly intuitive. The Condorcet criterion itself 
is defective, as can be shown by real-world examples, but it is 
*usually* telling.

When a Range election fails the Condorcet criterion, it indicates 
that there is either a compromise that involves a plurality of voters 
giving up a small benefit in order to provide a larger benefit to a 
smaller number, which real people routinely do when they understand 
the choice, *or* strategic or inaccurate voting has led to an 
*appearance* of this. Which is why resolving this with a much more 
direct comparison, the electorate now knowing the situation, in a 
runoff, is likely to fix rare problems.

Meanwhile, a voting system that is possibly as advanced as anything 
reasonably likely to see the light of public usage soon has been 
proposed in Arizona. It's far more sophisticated than meets the eye at first.

Existing system: top two runoff. Nonpartisan municipal elections. 
Primary 10 weeks before the general election. If no majority, runoff 
in general election. Both elections, vote for one. Write-ins may be 
allowed in both elections, I'm unclear about that. (But write-in 
candidates must meet certain criteria or the votes are not counted.)

Proposal (Arizona HB 2518):

Approval primary, 10 weeks before the general election. This is 
*only* a primary, it cannot complete (unless the electin is 
uncontested? Many of these are.) Top two candidates go to the general election.

There are some subtle features here that are easily missed by voting 
systems enthusiasts.

The law does not change any existing elections, it merely provide 
options. An IRV option was tacked on through FairVote intervention, 
making a very simple bill into a monstrosity that might violate the 
Arizona constitution. This was on track to pass in the Arizona 
Senate, having passed in the House. It is now unclear. FairVote has 
stated that Approval might be a decent method in certain kinds of 
elections, and these might fit their idea, but they forgot to 
communicate this to the President of FairVote Arizona, who is also 
the President of the Arizona League of Women Voters, who argued 
against the bill on the basis that Approval is Bad -- FairVote has 
written a lot that might make one think that, like LNH violation, 
which really doesn't apply here -- so ... the bill's sponsor decided 
to accept the monstrosity as a compromise. It may have been 
unnecessary. But ... he's on the ground there.