[EM] Why I think IRV isn't a serious alternative 2

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sun Dec 28 14:28:16 PST 2008

At 05:48 AM 12/28/2008, Kristofer Munsterhjelm wrote:
>Abd ul-Rahman Lomax wrote:
>>The error was in imagining that a single ballot could accomplish 
>>what takes two or more ballots. Even two ballots is a compromise, 
>>though, under the right conditions -- better primary methods -- not 
>>much of one.
>I think I understand your position now. Tell me if this is wrong: 
>you consider the iterative process of an assembly the gold standard, 
>as it were, so you say that all methods must involve some sort of 
>feedback within the method, because that is required to converge 
>towards a good choice.

It's not clear how close a method like Range can get to the idea in a 
single round. If any method could do it, it would be Range. It may 
depend on the sophistication of the electorate and its desire to have 
an overall satisfactory result. In what I consider mature societies, 
most people value consensus, they would rather see some result that 
is broadly accepted than one that is simply their primary favorite. 
What goes around comes around: they know that supporting this results 
in better results, averaged over many elections, *for them* as well 
as for others.

>  That feedback may be from one round to another, as with TTR, or 
> through external channels like polls, as with the "mutual 
> optimization" of Range.

>Is that right?

Yes. Polls or just general voter impressions from conversations, 
etc., "simulate* a first round, so voters may *tend* to vote with 
compromise already in mind. And that's important! That's called 
"strategic voting," and is treated as if it were a bad thing.

But, we know, systems that only consider preference are flat-out 
whacked by Arrow's Theorem. And once preference strength is involved, 
and we don't have a method in place of extracting "sincere 
preferences with strengths" from voters, we must accept that voters 
will vote normalized von Neumann-Morganstern utilities, not exactly 
normalized "sincere utilities," generally. Real voters will vote 
somewhere in between the VNM utilities -- incorrectly claimed to be 
Approval style voting -- and "fully sincere utilities."

Such a system is claimed by Dhillon and Mertens to be a unique 
solution to a set of Arrovian axioms that are very close to the 
original, simply modified as necessary to *allow* preference strength 
to be expressed.

But even a single stage runoff can introduce vast possibilities of 
improvements of the result. The sign that this might be needed is 
majority failure. ("Majority" must be defined in Range, there are a 
number of alternatives.) Range could, in theory, improve results even 
when a majority was found, but, again, we are making compromises for 
practicality. A majority explicitly accepting a result is considered 

(Asset can do better than this! But that's another argument for another day.)

>If you're going to use Bucklin, you've already gone preferential. 
>Bucklin isn't all that impressive, though, neither by criteria nor 
>by Yee. So why not find a better method, like most Condorcet 
>methods? If you want it to reduce appropriately to Approval, you 
>could have an "Approval criterion", like this:

Simplicity and prior use. I'm not convinced, as well, that realistic 
voter strategy was simulated. Bucklin is a phased Range method 
(specifically phased Approval, but you could have Range Bucklin, you 
lower the "approval cutoff," rating by rating, until a majority is found.

(I'll mention once again that Oklahoma passed a Range method, which 
would have been used and was only ruled unconstitutional because of 
the rather politically stupid move of requiring additional 
preferences or the first preference wouldn't be counted.)

No, Bucklin isn't theoretically optimal, but my suspicion is that 
actual preformance would be better than theory (i.e., what the 
simulations show.) Bucklin is a *decent* method from the simulations, so far.

(Most voters will truncate, probably two-thirds or so. If a 
simulation simply transfers preferences to the simulated ballots, 
Bucklin will be less accurately simulated. Truncation results in a 
kind of Range expression in the averages -- just as Approval does to 
some degree. The decision to truncate depends on preference strength.)

>If each voter has some set X he prefers to all the others, but are 
>indifferent to the members among X, there should be a way for him to 
>express this so that if this is true for all voters, the result of 
>the expressed votes is the same as if one had run an approval 
>election where each voter approved of his X-set.

A Range ballot provides the opportunity for this kind of expression. 
It's actually, potentially, a very accurate ballot. If it's Range 
100, it is unclear to me that we should provide an opportunity for 
the voter to claim that the voter prefers A to B, but wants to rate 
them both at, say, 100 -- or, for that matter, at any other level. 
What this means is that the voter must "spend* at least 1/100 of a 
vote to indicate a preference. That's practically trivial. (It could 
be argued that the "expense" should be higher. It's also possible 
that the Range ballot isn't linear -- Oklahoma was not. But I won't 
go there now.)

 From the Range ballot, once can infer ranked preferences (equal 
ranking allowed). There is no particular motivation to rank 
insincerely. What motivation exists for is "exaggerating" -- 
allegedly -- preference strength. If there is Condorcet analysis, 
then this is blunted just a little. Thus, if you have a significant 
preference, there is motivation to express it, either accurately or 
"just a little" or somewhere in between.

Borda essentially enforces this, the problem with Borda is that 
assumption of equal preference strength. It's been pointed out that 
with many candidates -- a "virtual candidate system" has been 
proposed -- Borda becomes, in effect, Range, very much like the Range 
I just proposed.

>All methods that satisfy this will be limited to the criterion 
>compliance of Approval itself, because criteria either pass or fail, 
>and if it's possible to force the method into Approval-mode, then 
>it's also possible to make the method fail any criteria that 
>Approval does fail.

Analysis of methods by criteria doesn't pass my criteria for 
criteria. Unless it's one of the SWF (Social Welfare Function) Criteria.

Does Approval pass the Majority Criterion? It depends heavily on the 
definition. And where it fails, it is quite arguable that it was the 
criterion that was defective, not the method....

>>Sure. Setting conditions for runoffs with a Condorcet method seems 
>>like a good idea to me. One basic possibility would be simple: A 
>>majority of voters should *approve* the winner. This is done by any 
>>of various devices; there could be a dummy candidate who is called 
>>"Approved." To indicate approval, this candidate would be ranked 
>>appropriately, all higher ranked candidates would be consider to 
>>get a vote for the purposes of determining a majority.
>So, an approval cutoff. For a sincere vote, what does "approved" 
>mean here? Is it subject to the same sort of ill definition (or in 
>your opinion, "non-unique nature") that a sincere vote for 
>straightforwards Approval has?

It has a very specific meaning for me: it means that the voter would 
rather see the approved candidate win than face the difficulties -- 
and risks -- of additional process.

It is a *decision*. Approval votes cannot be derived from a 
preference profile alone. They *can* be derived from Dhillon-Mertens 
normalized VNM utilities. That's why Dhillon and Mertens did propose 
Approval as a possible implementation of Rational Utilitarianism. 
Consider them rounded-off VNM utilities.

("VNM utilities" sounds complicated. It isn't, unless one insists on 
*numbers*. It's how we normally make decisions! We weight outcomes 
with probabilities. Instinctively.)

>>In Range, it could be pretty simple and could create a bit more 
>>accuracy in voting: consider a rating of midrange or higher to be 
>>approval. This doesn't directly affect the winner, except that it 
>>can trigger a runoff. Not ranking or rating sufficient candidates 
>>as approved can cause a need for a runoff. If voters prefer than to 
>>taking steps to find a decent compromise in the first ballot, *this 
>>should be their sovereign right.*
>>A Range ballot can be used for Condorcet analysis. Given the Range 
>>ballot, though, and that Range would tie very rarely, it seems 
>>reasonable to use highest Range rating in the Smith set, if there 
>>is a cycle, to resolve the cycle.
>Hm, this may work, or at least be better than Range. Since the 
>cardinal ballot is interpreted as an ordinal ballot - by rank as 
>well as by value - there's not as great an incentive to 
>compress-compromise. That still doesn't explain what the ratings of 
>a cardinal ballot actually mean, though, but inasfar as people have 
>an intuitive sense of what they do, it might work.

Yup. I think so.

Consider a Range ballot as a ladder of rankings. The candidates can 
be placed anywhere on the ladder, but voters will know that the full 
vote is expressed if one, at least, is at the top, and one, at least, 
is at the bottom. They will also know, quite instinctively, that if 
one cares about influencing the outcome, a preferred frontrunner 
should be placed close to the top -- or at the top -- and the worst 
frontrunner at or near the bottom. They will not vote stupidly as 
some Range critics have complained.

Very simple voter "strategy," call it "sincere compromise," will 
result in normal votes that are *close* to maximally effective. 
That's what I predict. But if they "distort," the result is Approval, 
essentially, which is quite a good method! But there is a cost to 
this for them: they lose expression of preferences that may be 
significant. So they will be restrained in this, I expect.

The bugaboo of Bucklin, multiple majorities, didn't happen, 
apparently, and won't happen except under very rare -- and very 
fortunate! -- circumstances. Bucklin satisfies all conceptions of the 
Majority Criterion if first rank votes must be single. (I don't like 
it, but there may be reasons to do this.) That removes a possible 
political objection. 3-rank Bucklin allows quite a bit more freedom 
of expression, even as it was implemented almost a century ago, than 
3-rank IRV.

And, as I mention, it's possible, then, with fairly minor tweaks, to 
move toward Range. If there is a Bucklin Range ballot, the ballot 
itself is a Range ballot, thus we are collecting that crucial data 
and we can monitor election performance. The door opens again.

And, hint to students: we don't know how and why Bucklin disappeared. 
What were the arguments? What was the politics? There were well over 
fifty cities, including San Francisco!, which implemented Bucklin. 
What happened?

One possibility: Bucklin, like IRV, was sold as a runoff replacement. 
When it was realized that sometimes, still, a majority was not found, 
that could have created a wedge against it. Watch what happens when 
it starts to be realized that the current cities which have 
implemented IRV have been snookered! They essentially replaced Top 
Two Runoff, which comes up with a better result than Plurality in 
maybe 10% of elections, with IRV, which almost always -- in these 
nonpartisan elections -- matches Plurality. They claimed that a 
majority would be found, when that claim was highly deceptive at best.

>>Thus we'd have these conditions for a runoff:
>>(1) Majority failure, the Range winner is a Condorcet winner. 
>>(probably the most common). Top two runoff, the top two range sums.
>>(2) Majority failure, the Range winner is not a Condorcet winner. 
>>TTR, Range and Condorcet winner (cycles resolved using range sum).
>>(3) Majority, both Condorcet and Range, but Range winner differs 
>>from Condorcet winner. same result as (2).
>>(4) Majority for Range winner, not for Condorcet. or the reverse. 
>>I'm not sure what to do about this, it might be the same, or the 
>>majority winner might be chosen. A little study would, I think, 
>>come up with the best solution.
>I think the easiest way would be to drop the probing of the 
>majority. Just have a two-candidate runoff between the CW candidate 
>and the Range candidate. If the two are the same, the second place 
>would be the second candidate of the social ordering of either the 
>Condorcet method or Range (unsure which). If there's no CW, discover 
>it by the tiebreaking system, or if that's too complex, by Range.

No, you probe the majority *to avoid runoffs*! If a majority has 
approved a winner, and there is no conflict, you are done. That's the 
normal outcome! (Unless you get *many* candidates.)

>There's also the somewhat strategy resistant variant that has been 
>proposed earlier: voters input ballots that rank some or all 
>candidates. All ranked candidates are considered "approved". Break 
>Condorcet cycles by most "approved" candidate (or devise something 
>with approval opposition to preserve clone independence, etc). The 
>point, at least as far as I understood it, is that you can't bury 
>without giving the candidates you're burying "approval", thus burial 
>is weakened.

Sure. That, in fact, is Bucklin! Ranking a candidate is approval of 
the candidate. (But Bucklin, itself, doesn't do Condorcet analysis.)

>>Want perfect? Asset Voting, which bypasses the whole election 
>>method mess! Single-vote ballot works fine! And that's what many or 
>>even most voters know how to do best.
>Or have a parliament and bypass the whole thing.

No, you still have the question of how to get the parliament. Asset 
Voting, actually, is the bypass. It can elect a parliament that is 
rigorously "proportional" -- more accurately, it is fully 
representative, with representation being created by free choices.

>>So I've shifted to proposing Bucklin, though Approval remains a 
>>simple, do-no-harm, cost-free reform. Introduce it to a TTR system, 
>>some runoffs may be avoided. Introduce Bucklin, more.
>Do you propose Bucklin because it gradually transforms to Approval 
>(as more ranks are counted), or because of its own properties?

I propose it because (1) it is cheap. (2) Yes, it phases into 
Approval as needed; in the first round, it elects the same candidate 
as Plurality *if* a majority is required and voters vote sincerely, 
and it's beyond me why they would not. (Even if multiple votes are 
allowed, it seems highly unlikely that voters with a significant 
preference would use them in the first rank.) (3) It's been used. (4) 
This is America, and it was known as American Preferential Voting. 
(5) It worked, we have a fair number of detailed examples of elections.

It's Approval, in effect, in many ways, but with that first 
preference expression that so many want. I don't like that one aspect 
of Approval! (I still believe Approval would work pretty well, 
because of who it is that would use the additional votes, but ... 
they, too, will dislike equating Nader with Gore, it will grate. The 
idea, though, that they wouldn't add a vote for Gore if they have a 
significant preference for Gore over Bush, on the theory that this 
might "harm* Nader, is preposterous. They would use those votes just 
as much as with IRV.)

>  If the former, the criterion I gave above might be useful if we 
> can find a method that is better on its own terms yet has that 
> property. If the latter, I think other methods are better. I'll 
> note, though, that it's quite easy to make a PR version of Bucklin 
> (and I've done so in an earlier post), so that claimed advantage of 
> IRV would also hold for Bucklin.

Sure. FairVote screwed up royally, hitching their sleigh, not to a 
star, but to a cinder, the *worst* kind of STV, single-winner, on the 
theory that it would pave the way. It could block the road!

Bucklin was used multiwinner, but I'm not sure that the method was 
optimal. Probably not. Could be done, though. Use Range ballots, though....

>>But Range Voting, a ranked form, was written into law in the U.S., 
>>I think it was about 1915. Dove v. Oglesby was the case, it's 
>>findable on the net. Lower ranked votes were assigned fractional 
>>values; I think it was 1/2 and 1/3. Relatively speaking, this would 
>>encourage additional ranking, I'd expect.
>By that reasoning, any and all weighted positional systems are 
>Range. Borda is Range with (n-1, n-2, n-3 ... 0). Plurality is Range 
>with (1, 0, 0, ... 0). Antiplurality is Range with (1, 1, 1, ..., 
>0), and so on.


Borda is *clearly* Range. Simply with a weird restriction. Likewise 
the others. Range with weird restrictions. But, here, I was following 
my classic analysis:

Plurality: Vote one full vote for one only. Candidate with the most votes wins.
Approval: Vote one full vote for as many candidates as desired. 
Candidate with the most votes wins.
Range: Approval with fractional votes allowed.

What fractional votes? That depends on the method. Nice one: 0, 1, 2, 
but expressed as -1, 0, 1.

Has a nice majoritarian interpretation: Candidate must get a positive 
vote to win.

Oklahoma was, I think, 0, 1/3, 1/2, 1.

(I'd have preferred, say, 0, 1/2, 2/3, 1, I think. Oklahoma gave too 
much weight to the first preference over the second.)

But, hey, we will have enough trouble getting full-vote Bucklin in 
place, enough trouble just to get jurisdictions to Count All the 
Votes, i.e., to use Open Voting or Approval.

More information about the Election-Methods mailing list