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

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> 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.

That makes the entire cycle, including polls and feedback, into one 
election system. Method is too narrow, because the system isn't just 
"input, then function, then output"; it doesn't just translate 
individual preferences into social preferences.

Thats all nice, but with the versatility of that wider definition, you 
get the chance of problems that accompany systems that include feedback 
within the system itself. Such can include cycling, and too much of 
either stability (reaches a "compromise" that wasn't really a good 
compromise) or instability (doesn't settle, as with cycling, or reaches 
a near-random result depending on the initial state of the system).

In short, there's a wider range of possible outcomes because the system 
permits many more configurations than a simple one-shot election method. 
This is good when it leads to a better result from voters optimizing 
their votes in a way that reaches the true compromise, but it's bad when 
factions use that increased range to try to game the system. If Range 
voters (for instance) need to consult polls or the prevailing atmosphere 
to gain knowledge of how to express their votes, then that too is 
something the strategists can manipulate.

When one uses strategy to construct a wider mechanism on top of a single 
election method by adding a feedback system (such as one may say is done 
by Range if it's used honestly), then that's good; but if one uses 
strategy to pull the method on which the system is based in a direction 
that benefits one's own preferences at the expense of others, giving 
oneself additional power, then that is bad. Even worse is if many 
factions do so and the system degrades further because it can't 
stabilize or because the noise swamps it; or if the combined 
strategizing leads to a result that's worse for all (chicken-race dynamics).

I think that what we have to distinguish here is Range as part of the 
wider system that involves adaptation, and Range as an isolated method. 
If you consider Range as an isolated method like other methods, which 
gathers information from voters, churn it through some function, and 
outputs an aggregate ballot ("society's ballot"), be it ordinal, 
cardinal or some other format, then Range is susceptible to strategy - 
the kind of strategy that leads to bad outcomes. However, if it's just 
one component of a wider system - the feedback method - then it becomes 
a sort of manual DSV that polls the intent of the voters (if they don't 
lie or drive it into oscillation etc), and that "greater method" may be 
a good one. I don't know.

 From a convenience point of view, some voters may want not to have to 
care about other voters' positions. "I just want to give my preference", 
says a (hypothetical) Nader voter who, although a third party supporter, 
  thinks Bush is so bad that among two-party mediocrity, Gore would be 
preferrable to Bush. Of course, if your point that people naturally vote 
VNM utilities (or somewhere in between those and sincere utilities) is 
true, then it would be an inconvenience to ask sincere cardinal opinions 
of voters, rather than the other way around. In any case, ranked methods 
  handle this issue, but note that the ranked methods are once-through 
methods, not part of a "manual DSV" system.

> 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.

Systems that only consider preference are "whacked" by Arrow's Theorem 
to the degree that the best methods come short of it. If we have "IIA 
except in a few cases", then that may be good enough. It is true, 
though, that all ranked methods are susceptible to strategy 
(Gibbard-Satterthwaite).

> 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 
> sufficient.

If a Range vote is a vote with a lesser strength, then Range fails 
Majority. If it's a partial vote, it doesn't. I think.

>> 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.)

Since we don't have programs to check how often various methods fail 
different criteria, I'll grant the part about criteria. However, Yee 
diagrams show very simple voting situations: there are candidates in 
"issue space" and people prefer candidates closer to them to candidates 
farther away. The Gaussian distribution of voters on a point might be 
contested, but that's about it. Bucklin produces quite strange Yee 
diagrams (though not the fragmented mess of IRV), so I'd say that if we 
had the chance to switch to another method, Condorcet would be quite a 
bit better at only slightly greater complexity (unless you want to go 
all the way to Schulze).

>> 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.)

Yes, Range passes that criterion, since voters can vote "Approval 
style". I also think Bucklin and QLTD passes it.

>  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.

If you have Condorcet analysis, the incentive to exaggerate is to say A 
(100) > B (99) > C (1) > D (0) instead of, for instance, A > B (75) > C 
(30) > D (2). If it's CWP, the picture gets more complex as I'm not sure 
what the optimal strategy is there. If you use the "Approval plus 
Condorcet rank, no ordering among disapproved", then there's not much 
incentive to exaggerate among the approved; instead, the strategy 
involves setting the Approval cutoff just right.

> 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.

There would have to be virtual candidates, and those virtual candidates 
would never be elected (even if one of them got highest Borda score). 
Otherwise, Borda's extreme weakness to burying would come into play and 
people would do

[favorite] > [nobodies] > [opponent]

which would lead to one of the nobodies winning if people disagree about 
favorites.

>>> 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.)

Okay, but if you're going to use VNM utilities, don't you need to put 
the election method inside a greater feedback system so that they 
normalize correctly?

> 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.

I've snipped most of the paragraph as I think I've answered it with my 
attempt to distinguish once-through methods from those that need 
explicit feedback. As an aside, I wonder how one would aggregate and 
publish the data so that ballots can't be used as "fingerprints" in vote 
selling. Fingerprinting would be like this: someone tells you to vote Y 
at value 63% (and all others at specified other values). They then go 
and check if any such ballot was registered. Since cardinal ballots are 
fine-grained, the chance of collision is slight. Hm, that may be an 
interesting algorithmic problem - it would probably involve rounding off 
the votes so that there are at least p ballots with the same 
(rounded-off) value for the same candidate...

>> 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.)

It's not really Bucklin, since the approval is in one go of all the 
candidates you ranked, whereas in Bucklin, the approvals are added in as 
the method proceeds. The approval cutoff would be - for sincere votes, 
at least - "these are good enough that I want to distinguish between 
them, but those are all bad".

>>> 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.

If you have a parliament, you can use a multiwinner method. Multiwinner 
methods are also vulnerable, but absent consistent errors (vote 
management), distortion in what winners it picks is not as bad as with 
single winner methods. If a single candidate gets replaced by someone 
else in a council of 100, that's 1% error. If a single candidate gets 
replaced by someone else in a single-winner election, there is no 
greater error (except if the candidate was replaced by an even worse one).

> 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....

I'm not sure how Range Bucklin could be turned into a multiwinner 
method. My multiwinner version of Bucklin is this: Keep adding votes 
until someone exceeds a Droop quota. Elect the person and reweight the 
strength of those who contributed to his victory, according to this 
formula: (new weight = old weight * (votes for winner - quota)/(votes
for winner)). Then remove the winner from all ballots and restart the count.

As an example, say there's an election for three candidates out of four. 
A wins the first count, then the voters are reweighted. The election is 
turned into "A wins, plus [election for two candidates out of three]". 
Nicely recursive.

The problem with Range Bucklin is that we're no longer certain that the 
votes *can* sum up to the Droop quota. Consider the case where all 
voters use non-normalized cardinal ballots and nobody's maximum range 
exceeds 1/10 of max score. The scores may well never reach the Droop quota.

>>> 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.
> 
> Yes.
> 
> 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.

If it's Range with restrictions, I don't think it would be Range 
anymore. Plurality is Condorcet with the restriction that you can only 
vote for one.

> 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.

That sounds like Nauru Borda. Nauru's version of Borda had first place 
count 1 point, second 1/2, third 1/3, and so on.