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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Thu Jan 14 16:46:45 PST 2010

```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
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.

```