[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Abd ul-Rahman Lomax]

At 12:51 PM 1/14/2010, Chris Benham wrote:
>I'm not sure what Kathy means by a "majority favorite".

Yeah, she's not necessarily precise, being a voting security expert, 
not a voting systems expert.

>That phrase is
>usually taken to refer to a candidate that is strictly top-ranked by more
>than half the voters.

There are other possible interpretations, especially if equal ranking 
is involved. We must take equal ranking as equal ranking, I claim, 
the voter  has decided that, even if the candidate isn't the strict 
favorite, the preference strength is low enough that the voter 
decides, under the circumstances, to conceal it and to apply equal 
voting power to both candidates.

The usage of voting systems criteria based on concealed preferences 
is fraught with hazard, it produces results that don't really 
correspond to real-world performance or value.

>  The "Majority Favorite" criterion is met by IRV and
>Plurality among many others, but not by Borda or Range.

No method passes the Majority favorite criterion if the voters don't 
vote strict preference, with a full-power vote. Borda and Range allow 
voters to express weak votes. If the "strict preference" described is 
expressed with weak votes, then, sure, the majority criterion fails. 
Consider this.

It's a Range 100 election. Half plus 1 voter votes this way:

A: 1, B: 0, C: 0.

What is the meaning of this vote? Unless half the voters are stupid, 
rather unlikely, it means that they dislike, almost fully, A, B, and 
C. These are really votes *against* all three candidates, but just 
not quite as strongly against A, who gets 1/100 vote.

Now come the rest of the voters, who vote this way:

A: 1, B: 0, C: 100.

The result is C. I would guess that if an approval cutoff is part of 
the method, say it's midrange, there will be majority failure as per 
the rules, because we are looking at a majority expressing a vote 
*against* A (unanimity, actually!), but the conditions of the 
Majority Criterion were set up only to consider pure ranking, not 
approval or preference strength or Yes/No or For/Against.

So, Yes, the majority criterion fails. By using examples that are 
closer to reality than this extreme example, it is made to appear 
that there is a serious criterion failure, but that depends upon an 
interpretation of the criterion that didn't at all consider 
preference strength or approval status, and the latter is crucial in 
traditional deliberative elections, the bedrock of democracy. A truly 
democratic organization does *nothing* with the explicit approval of 
a majority, excepting situations where an officer states an intention 
to rule absent objection, where the approval isn't necessarily 
explicit but can be assumed. No election is valid in such 
organizations without a vote from a majority of those voting 
approving of the result.

If any voting system makes general use of approval status (to 
determine majority acceptance of the result) or preference strength 
(to give more weight to strong preferences than to weak ones, which 
clearly makes sense when voting is based on actual utilities), it 
will fail the Majority Criterion as written previously, before Range 
was on the table. And when voting systems experts were paying no 
attention at all to repeated balloting, it wasn't even considered an 
election method because it isn't deterministic. And, note: there goes 
Arrow's theorem and the rest of the impossibility theorems, they 
depend on the method being deterministic, and some other 
characteristics that require new interpretations, such as 
Independence from Irrelevant Alternatives.

(A voting system should obviously be independent of irrelevant 
alternatives. The problem is that voters aren't. If voters modify 
their preference strength expressions based on some perception of 
strategic value, then the presence of an irrelevant candidate can -- 
if the voters misjudge the situation -- alter the results. Range with 
so-called "sincere votes" does obey IIA, and if voters would vote 
these sincere votes, in most situations they would get optimal 
results. If there were a way to weight votes according to overall 
preference strength, there would be *no* situation where there is a 
violation. In studying IIA as it applies to ranked voting systems, 
it's assumed that the voters vote their sincere preferences. So, the 
analogous vote with a range system would be the sincere vote.

But this is the problem. Normalization. Normalization, however, is a 
voting strategy that is voluntary. In order to make Range fail, a 
candidate must be introduced who alters the normalization strategy by 
extending the range. (Or with removal by reducing it.) And then this 
example is asserted as a violation of Range. But with any system, if 
the voters alter their vote by the presence of an irrelevant 
alternative, the system will fail IIA.

I presume this is why Warren Smith claims that Range satisfies IIA 
"under some interpretations.

>I am sure the majority of voters whose favourite was A in my examples
>would be very pleased that they were "allowed to participate in all the
>rounds".
>
>Is being "monotonic" more important than satisfying  Majority Favorite?

I'll answer that. They are both quite important, fundamental, I'd 
say. But the application must be understood. First of all, they must 
deal with votes as writ, not as concealed, because concealed 
preferences can make any system fail any criterion.

If concealed preferences are going to be used, it better be clear why 
this is damaging, for the criterion to have any importance. 
Plurality, for example, encourages voters to conceal, too often, a 
very important preference, their first preference. But the Majority 
criterion considers that, when it's worded to refer to the expression 
of strict preference.

However, to extend this to Range voting, we have to further specify 
that this is a full-strength vote, because, obviously, if the 
majority casts a weak vote, it is no longer equivalent to the votes 
of the minority. An example:

51: A:100 B: 99 C:0
49: A:  0 B:100 C:0

This election will fail a certain interpretation of IIA and, as well, 
the majority criterion. However, look at the substance. Let's suppose 
that C is a real candidate who is actually not a bad choice, he just 
has the bad luck to face two better candidates. So when the A voters 
vote A:100, B:99, the votes have a clear meaning: A and B are really 
both very good choices. The A voters will be quite happy with the 
election of B, even though their "first preference" was not chosen.

And lets assume, as well, that all these voters are sincere. And, 
indeed, from votes, we must assume that, it's a tricky and dangerous 
assertion, to be handled with caution, to assume that they are not. 
Likewise, we must assume that the A voters know what they are doing 
when they voted as they voted. Just as we must assume that Nader 
voters in Florida knew what they were doing when they voted for Nader 
instead of Gore. They surely knew, in general, that they thereby 
risked the victory of Bush, and, contrary to what many have asserted, 
my conclusion is that they didn't consider that a disaster. Until 
later! And, sorry, no voting system is going to protect people 
against stupid decisions.

(My point doesn't depend on some idea of Nader voters being stupid. 
The opposite, actually, whether or not they were "wrong" in some 
sense. My general principle is to give voters as full a power of 
expression as practical, and to use that information to generate 
optimal results, based largely on maximizing social utility as can be 
determined through simulations, as well as the study of actual 
elections. This isn't about Progressive or Liberal or Conservative or 
whatever the right-of-conservative calls itself. Or Libertarian, 
which doesn't fit into right-left.)

If those votes represented actual values to the voters, perhaps what 
tax they'd be willing to pay for the election of a candidate, we'd 
maximize value, quite clearly, by violating this shallow majority 
criterion, not designed to handle weak votes.

But if a voting system violates a deeper statement of the majority 
criterion, it's a big deal. And IRV does.

>Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic?

This opinion, stated as fact, is false. Top Two Runoff is a two-step 
system, and monotonicity doesn't refer to such. It refers to the 
effect of a vote on a single ballot as to the result of that ballot 
only. A vote for a candidate on a primary ballot in TTR will always 
help the candidate supported to make it either to a majority and a 
win, or to make it into the runoff. It never hurts that candidate. 
Something else may, and some other vote on the part of that voter may 
indeed be more effective, for some set of voters. A strategy, an 
insincere vote. But very dangerous, for if all voters vote in this 
way, that is, those who raise a turkey in order to help their 
favorite win the runoff, the favorite doesn't get any votes in the 
primary and doesn't make it to the runoff. They have to have enough 
votes to make it to the runoff, and, then, to push the turkey up over 
their serious opponent, who would win in a runoff. This is so tricky 
that I'm not sure it's ever been actually done. Did supporters of the 
Lizard vote for the Wizard in order to create the Lizard vs. Wizard 
election in Louisiana? I rather doubt it. But this wouldn't create a 
monotonicity violation, and the problem is created by eliminations, 
it doesn't exist with repeated balloting.

The point is that TTR is really two elections, and the term covers at 
least two variations, as to actual systems in use, and even more if 
advanced methods are considered. Does anyone doubt that the 
*effective election,* the one that results in a winner, with any TTR 
eletion, if we assume plurality rules in the primary and runoff, is 
monotonic? Complicating this is that the voter may be casting one or 
two votes. The voters in the second election are not the same set of 
people as in the first. I've never seen a voting systems expert other 
than myself (if I'm to be considered an expert, which is ... arguable 
but somewhat shaky, my knowledge has big holes in it) who has 
considered the effect of turnout on social utility.

But let's do what is too often not done. Is there any truth to 
Chris's statement? What if we consider Top Two Runoff as a single 
election process. Let's simplify it and run it as an immediate 
two-step process. The same voters. This, of course, removes much of 
the real value and reform character of Top Two Runoff, but let's set 
that aside.

I'm sorry, I don't get it. Not quickly, anyway, or not for sure. The 
strategy I know is turkey-raising, which doesn't involve a 
monotonicity violation, it violates Favorite Betrayal. And we know 
that TTR is vulnerable to center squeeze, so it violates the 
Condorcet Criterion. Notice that both of these criteria involve, with 
TTR/Majority/Plurality 2, considering concealed preferences....

(I'm going to start referencing TTR with a specification of the 
method used for each round. So we might have, for example, 
TTR/Bucklin/Bucklin 2, which wouldn't fully specify the method, but 
might give an idea. Bucklin 2 means Bucklin with 2 candidates allowed 
on the ballot. It's useless unless write-in votes are allowed or 
majority failure is otherwise possible.)

Let me go through this. A vote for a candidate in any of the 
mentioned TTR systems, in the primary, can only help the candidate 
win or get into the runoff. It can never prevent that candidate from 
attaining one of these two goals. Monotonic. A vote for a candidate 
in the runoff is the same. Monotonic. By what interpretation could a 
vote be considered to harm the candidate voted for?

Here would be the argument, I'd guess. The voter prefers A>B>C. The 
voter fears that B will make it into the runoff, and that A would 
lose. The voter can vote for C, and perhaps C will instead make it 
into the runoff. So the vote for A, it can be argued, harms A. But it 
is a harm of omission. It's not the vote for A that harms A, for this 
helps A make it into the runoff. It's the lack of (insincere) support 
for C that causes the supposed harm to A. Does this match the 
*intention* of the monotonicity criterion?

I don't think so. That some superior strategy exists to a vote for A 
doesn't make the A vote harmful. And, we might note, the turkey 
raising strategy mentioned could backfire, completely eliminating A 
from the runoff, if enough voters do it. The "harm" is only from the 
point of view of the A voter, and if A instead votes for C, the 
intention is clearly to harm the overall result, because the voter is 
trying to get A to win when, in fact, the electorate prefers B to A. 
Turkey raising makes no sense outside this narrow and selfish 
political strategy.

So, if the voter votes sincerely, as almost all voters naturally will 
in a situation like this (three viable candidates, plurality method), 
A and B go into the runoff, and A wins the runoff, will the voter 
then be kicking himself, "damn! If I and a few voters would have just 
voted for C, we'd have had a runoff between A and C, with a shoe-in 
for A! What a terrible voting system this is!"

I doubt that one person would think that, and they certainly would 
not blame the system! But monotonicity failure certainly can and will 
produce serious voter disrespect for the system. With true 
monotonicity failure, a single vote on a ballot harms the candidate 
the voter actually voted for. This is so seriously in opposition to 
what voters have come to expect for elections that, once widely 
known, I doubt that a voting system which is not monotonic will 
survive, if any examples of such failure come to light, and they 
involve significant numbers of voters. Ahem. Burlington, Vermont, 
2009 Mayoral election. I'd say that IRV in Burlington is toast.

So the net result of foolish reform could be regression and an 
obstacle to reform for many years. Think about it. If we are going to 
reform a system, shouldn't we be careful about how we do it, study 
the options, solicit as much comment as possible and create 
mechanisms to filter and weigh it. Or should we just depend on 
outsiders to come in and organize us with some proposal that they 
want for their own reasons (for better or worse), and who are 
political activists who have a specific agenda and to hell with any 
other possibility?

We in the voting systems community attempted for years to engage with 
FairVote and were blown off with dismissals as ivory-tower nut cases, 
politically naive. Them chickens are coming home to roost. By 
excluding expert opinion, FairVote just may have blown a tremendous 
opportunity by focusing on a defective reform in spite of all the 
obvious criticism, by selling it based on deceptive arguments that, 
indeed, are being exposed right and left as people wake up.

"Find a majority without runoff elections." They might as well have 
said, "Free Pie. In the Sky." There is no way to reliably find 
majorities without runoff elections, unless you coerce the voters in 
some way. You can *reduce* the need for majorities, using an advanced 
voting system, and IRV does seem to do this, sometimes, a little 
better than Plurality. But with nonpartisan elections, it doesn't 
really change the results, whereas when majority failure occurs in a 
top two runoff election, it does indicate a need for more 
consideration and sometimes -- one time in three -- that 
consideration flips the result from what IRV almost certainly would 
have decided if used. Which is almost always the Plurality result.

"Reduce negative campaigning." Sounds good, eh? Except it's 
meaningless, there is no evidence that this actually happens except 
to some small degree with minor candidates with no chance of winning, 
who do sometimes cooperate with each other to gain lower preference 
votes. Not to win, but just to come up with a possible better 
showing. That's nice, sure. But the big noise in campaigns don't come 
from them, they come from frontrunners, who don't have that motive to 
cooperate, the system encourages them to increase their own 
popularity and to decrease that of any serious opponent.

Can we imagine Bush holding a joint meeting with Gore to try to get 
voters for one to add a second preference vote for the other?

Sure, I could imagine, perhaps, Gore doing this with Nader. Maybe. 
But the negative campaining that people don't like takes place 
between the frontrunners. And any good system, not just IRV, would 
quite adequately encourage that. Bucklin has a somewhat less strong 
incentive to add second-rank votes, particularly if there is strong 
preference for the frontrunner. (True for Range and Approval as 
well). But I'd still not expect serious make-nice between 
frontrunners, only with minor candidates, to try to get their 
supporters to add lower ranked votes. And it can backfire, and, in 
fact, I think there was a Bucklin election where it did. The 
candidate tried to woo what became a seriously unpopular interest 
group, and it was publicized, and probably contributed to his loss. I 
think the election was Bucklin, I think he was the incumbent, in 
Cleveland, I should look this up.

"Allow voters to vote sincerely." Bucklin actually does this, but IRV 
punishes some sincere voters.

People will remember the IRV fiasco, and will tar all election reform 
with the gooey sticky mess FairVote created. Fortunately, they 
weren't all that successful, so there is still room with places that 
might try simpler and better reforms.

Like, duh, Count All the Votes, which is astonishingly powerful if 
applied to existing voting systems. Just toss the overvoting rules 
and count all the votes. Instant Approval, no fuss, no muss, no harm, 
and, suddenly, no first-order spoiler effect. Florida 2000 Nader 
voters suddenly have a new option: an additional vote for Gore.

But I think that option is more likely to be exercised if it's 
ranked, hence Bucklin. That's what it is, invented more than a 
century ago, and worthy of serious attention. Perfect voting system? 
No. But damn good. And simple. And easy to understand and canvass. 
And, then, easily tweaked to make it even better. And since there is 
practically no implementation cost, there is really no harm even if 
it is later decided to dump it. There is *truly* no cost with 
Approval, just a tweak in the ballot instructions. No change in 
counting equipment because all voting systems equipment can already 
handle it. No change in the rest of the ballot for approval, small 
change for Bucklin (as many extra voting positions per candidate as 
there are ranks to be used. Bucklin would be decent with one extra 
rank, and just about thoroughly sufficient with two.

Look, I think it's obvious. But, at least, it should be tried! We 
already knew that IRV was punk, and this was known over a hundred 
years ago. But who pays attention to history and academic study from 
the late nineteenth century? Certainly not the powers that were in 
Australia, who implemented IRV to save their rear ends from the 
spoiler effect. I think they knew exactly what they were doing.