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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Tue Dec 30 19:49:38 PST 2008

At 12:46 PM 12/30/2008, Kristofer Munsterhjelm wrote:
>Abd ul-Rahman Lomax wrote:
>>At 05:48 AM 12/28/2008, Kristofer Munsterhjelm wrote:
>>>Abd ul-Rahman Lomax wrote:
>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.

"Election systems" in the real world are extraordinarily complex. 
"Voting systems" are methods for taking a ballot and generating a 
result; sometimes this is a fixed and final result, sometimes it is 
feedback for subsequent process, which may include a complete 
repetition, repetition with some restrictions, or even a coin toss.

Individual preferences do not exist in a vacuum, there is inherent 
and massive feedback in real societies. The idea that there are these 
isolated voters who don't talk to each other and don't influence each 
other by their positions is ... ivory tower, useful for examining 
certain theoretical characteristics of systems, but not for 
predicting the function of systems in the real world. It can be 
useful, sometimes, but we must remember the limits on that utility as well.

>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).

We are now considering as relevant "cycling" within the entire 
electorate, within the process by which a whole society comes to an 
election with the set of preferences and preference strengths that 
they have. Human societies have been dealing with this for a long, 
long time, and the best answers we have so far are incorporated in 
traditional deliberative process, which insures that every point of 
view of significance is heard, that possible compromises are 
explored, and that there is an overall agreement that it is time to 
make a decision, before the decision is actually made. And then the 
decision is generally made by or with the explicit consent of a 
majority of those voting, with the implicit consent of those not 
voting (but able to vote).

>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.

Range voters don't need to consult polls! They can do quite well, 
approaching the most strategic possible vote, without them, voting 
purely based on their opinions of the candidates and some common sense.

Those who strategize, who do something stronger than this, are taking 
risks. All the groups will include people who strategize....

>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)

The "pulling" of a group toward its preferred result is, however, 
what we ask voters to do! Tell us what you want, and indicate by your 
votes how strongly you want it! Want A or you are going to revolt? 
You can say that, perhaps, though we are only going to give you one 
full vote to do it with. Want to pretend that you will revolt? -- or 
merely your situation is such that A is so much better than the 
others that you don't want to dilute the vote for A against anyone by 
giving them your vote? Fine. That's your choice. It helps the system 
make its decision.

Be aware that if the result is not going to be A, you have abstained 
from the result. If there is majority failure, you may still be able 
to choose between others. (IRV *enforces* this, you don't get to cast 
a further vote unless your candidate is eliminated.)

*Truncation will be normal*. And, in fact, represents a reasonably 
sincere vote for most voters! (In most common elections under common 
conditions). Why are these "strategic voters" different.

I realized the error quite some time back in connection with Approval 
voters. The votes are "strategic" because the voters supposedly "also 
approve" of the candidates, but for "strategic" reasons, don't also 
vote for this supposedly also-approved candidate. But "approval" 
isn't an absolute. There is no absolute "approval cutoff." What we 
approve depends on what we think we can get!

Saari and some other voting theorists strongly dislike the 
indeterminacy of this? How are we supposed to do our nice neat 
analyses of how voters will vote, based on our suppositions regarding 
their preferences, if they will shift their votes depending on how 
they perceive each other, as well as the candidates.

But isn't this the decision that voters are *really* making? What is 
the best outcome for *this* electorate? Paradoxically, it is alleged 
that voters will elect mediocre candidates. Why? Because, supposedly, 
they will vote for any candidate who is above, even if just barely, 
the average. It's preposterous! We don't and won't vote that way! 
I.e., if voters vote "sincerely," as these analysts imagine (together 
with imagining what the "sincere vote" is), of course they will get a 
mediocre outcome (often)! But that voters *don't* just rubber-stamp 
candidates, *won't* add additional preferences or approvals unless 
they are willing to support the election of these additional 
candidates, causes the method to work. *Strategic voting is necessary!*

Arrow and others saw the problem with utilities and cardinal ratings 
as being that there were no absolutes, no single way to translate a 
set of utilities into a voting pattern. It turns out this that wasn't 
a *problem,* it was necessary for the voters to have this freedom, to 
use probability information in addition to raw, isolated, what-if 
utilities. And this is how we individually make decisions in our 
lives. We do not just go for the best possible imaginable option, we 
moderate that and go for what we think we can get. Good thing, too!

But there is nothing wrong with aiming a little high. And when too 
many voters aim too high, we get majority failure, which means that 
the voters need to reconsider a bit. Ideally, the approval cutoffs 
slide down a little. That's what happens with deliberative process; 
we can approach this with election methods, and I think that it's 
possible to get quite close with two rounds, provided the rules are 
right. What I've come up with so far is using an advanced method for 
the primary, and probably for the runoff as well, because I also want 
to see write-in votes being possible in the runoff, in addition to at 
least two candidates on the runoff ballot. We actually have this.... 
without the advanced methods. Majority required in the primary, 
plurality is allowed in the runoff. A runoff is only held when it is 
arguable from the election results that *either* candidate on the 
ballot might be a decent choice, perhaps from different perspectives 
(Range winner vs. Condorcet winner). Majority failure is a reasonable 
runoff trigger, but some runoffs are more reasonable than others. For 
example, a primary with three candidates, A, B, and C, with A getting 
49% of the vote, B, 26, C, 25, really doesn't need a runoff, if this 
was a preferential ballot, those are percentages after transfers or 
additions, and voters could have dealt with the situation that B and 
C were vote-splitting. Thus it *may* be possible to set some 
conditions that will sometimes avoid unnecessary runoffs. But I would 
not like these conditions to be anything other than very reasonable 
and solid predictions, based on the expressed votes., that the winner 
would gain a majority in the runoff.

It all becomes unnecessary with Asset. The "runoff" is an election 
process in which only the public voters, those who collectively 
represent all the voters in the primary, vote.

Asset is the only system where voters can vote with *total* 
sincerity, not voting for any candidate whom they do not maximally 
trust, can bullet vote if they want, and lose no participation in the 
result. They will know where their personal vote went. (If was 
single-winner, and also if it was multiwinner and electors take care 
to reassign votes by precinct (substantially).

>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.

Sure. But then we think of Range as a kind of blind poll, where the 
electorate has no sense of itself.

>  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.

"Susceptible to strategy" must be understood in the context; it means 
something different with Range than it does with ranked methods. And, 
I'd submit, it does *not* lead to bad outcomes.

Strategic voting in Range, in theory, damages the outcome. But 
compared to what? Compared to so-called "sincere" votes. This seems 
necessary because the very method by which we judge the outcome 
quality is the sum of "sincere utilities." However, there is a 
problem. Sincere utilities are not votes; votes are typically normalized.

I've seen a result from Warren Smith that, if I read it correctly, 
showed better simulation outcome with a *mix* of so-called sincere 
and so-called strategic votes.

What? Range isn't ideal? That's right. To get ideal results we would 
need to have some way for voters to not only know absolute, 
commensurable utilities, but to be required or incentivized, somehow, 
to vote them. There can be such methods, typically using auctions.

However, Range itself, in practice, is a kind of auction. The voter 
has a vote to spend. Let the voter spend this vote how the voter sees 
fit. The voter can place the entire vote in one basket, so to speak. 
That's a bullet vote for one candidate, 100%, against all other 
candidates, 0%. Or, strategically the same, the same vote but with 
intermediate votes where the voter sees them as harmless or even of 
non-electoral benefit.

Now, where is the "harm?" Well, obviously, if a voter knows that the 
voter's vote will affect the outcome, the voter can choose the basket 
to invest in that will cause the best outcome. But, in fact, the 
voter doesn't know the outcome, or not well enough to make exact 
predictions. Where the voter *does* have that kind of knowledge, 
strategy doesn't make much difference.

What is happening is that the voter won't add an additional 
"approval," if the voter fears that this will damage the outcome from 
the voter's perspective. And the result might be the election of the 
voter's favorite. But only if the rest of the electorate, basically a 
majority or, under Range, the weight of overall preference, agrees!

Strategic voting in Range is what would be sincere expression of 
strong preference in a ranked method. Prefer A over all others and 
don't give a fig about the others if A is going to lose? Vote for A 
and truncate. It seems that many or even most voters will do this if 
allowed. I really need to look at those San Francisco ballot images, 
they have stories to tell that don't show in the election results. 
What is the level of truncation? We know how many voters for minor 
candidates truncate -- or maybe run out of ranks -- before reaching a 
frontrunner, *lots* of them. But what we don't know is how many 
supporters of major candidates (top two) truncate. Its' not generally counted.

>  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.

Plurality works much better than we might think because of the 
greater system. It's still pretty bad! But *usually* it comes up with 
the right result! And when it fails to do that, *usually* the result 
isn't terrible. I don't know how much longer we can depend on 
"usually" being good enough!

> 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.

People vote vNM utilities, that's pretty obvious. A vNM utility is 
somewhere between a "sincere normalized utility" vote and an 
approval-style vote.

It's not inconvenient to be *allowed* to vote intermediate utilities, 
it is not a requirement. A voter might vote 100% for their favorite 
and, with sum-of-votes range, they are done. And in most elections, 
this is all most voters need to do! And the rest know, usually, who they are.

Range is nothing more or less than allowing fractional votes. Voters 
don't have to use them!

>  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.

Ranked methods, though, suffer from *two* problems. We've been 
discussing the problem of loss of preference strength information, 
but there is another: the very serious difficulty that many voters 
face in trying to fully rank. This is why Carroll invented Asset: to 
allow voters to, if it is what they wanted to do, simply vote for 
their favorite without losing voting power.

>>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 

Sure. But pure ranked methods *all* suffer from the two very serious 
problems I mentioned. A preference profile, a true profile, is not 
purely ranked. That's not how the human mind operates.

Ranked methods used as primary stage in a runoff system, though, 
don't suffer nearly as much from these problems.

>>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.

Range itself is generally considered to fail Majority; however, there 
is a problem with definitions. If a voter has the "exclusive 
preference" that is the basis for "majority preference," but does not 
vote this preference, then no method can detect an unexpressed 
preference. However, on the other side, and with Range Voting I 
consider it telling, we can argue that if a majority has ranked a 
candidate higher than all others, it has expressed the necessary 
preference. Now, if this triggers a runoff (because a different 
candidate has a higher total, and the runoff method is clearly MC 
compliant, then the system becomes MC compliant, as long as we 
consider the necessary majority to refer to the last election in the 
overall process.

>>>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).

I should look at the Yee diagrams. Bucklin incorporates a certain 
discontinuity because of the fact that a majority can occur at 
different integrations of the ranks. Bucklin, aside from that, 
though, is Approval, with a device that probably will encourage 
sincere voting. Yee diagrams don't show social utility, they show 
possible chaos in results. IRV not being monotonic is indeed a mess. 
But Bucklin is monotonic.

To really judge Bucklin's performance requires a better simulation of 
"additional approval." In real elections, the decision to add 
additional preferences is a complex one. You cannot simply assume, 
for example, that voters will use all the ranks. Most won't. Most, 
apparently, won't even use the second rank. And that makes perfect 
sense, and shouldn't harm outcomes! The only problem arises when the 
method terminates with a plurality.

We've made a mistake in considering Plurality a method, it is a 
*class* of methods, or a specific election rule. Almost all methods 
generally proposed, excepting those which incorporate runoffs, are 
plurality methods. Even full-ranking required methods produce a 
majority only by coercing voters into voting for all but one 
candidate; the "majority" which is, then, necessarily produced is not 
one coming from free consent to the election.

A Condorcet method with voluntary ranking, though, could certainly be 
used as a primary for possible runoff. With voluntary ranking, we 
could either assume that voters, by ranking a candidate, are 
consenting to the election (in which case it is a kind of ranked 
approval, in a sense), or a dummy candidate can be used to indicate 
the approval cutoff in the preference order, which is technically 
superior because it allows voters to express preferences between 
unapproved candidates.

>>>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).

Sure. Except what is the "instead of" set of ratings? I think we need 
to remember that these are *votes* and *not* sentiments. "Ratings" is 
a convenient way to talk about fractional votes, but what the voter 
is doing is expressing some combination of utility and probability 
assessment. The voter wants, naturally, to put votes where they 
count, where they make a difference. The voting pattern described -- 
both of them -- preserve preference order; however, the voter, with 
the first pattern, we may speculate, sees the important pairwise 
election as involving the (A,B) vs (C,D) pair, we can't really tell 
more than that. The voter prefers A but quite clearly is willing to 
accept B. B might be a frontrunner. If C is a frontrunner, that 
would, as well, explain the low vote of 1 point. In Approval, it's 
obvious how this voter would vote. If there is a runoff that 
considers pairwise preference expression, there is then some 
motivation to allocate that 1 point in order to express a preference, 
just in case -- or for independent reasons, such as the allocation of 
ballot position in future elections, or public campaign funding.

The voters are in control of the input to the system; they are making 
*decisions,* not expressing preferences as such. They are tossing 
weights on a set of scales according to some simple rules. Toss 
anything from nothing up to one full vote's weight in each 
candidate's scale. Candidate with the most weight wins.

Condorcet analysis, added to a Range system, incentivises, not 
exaggeration, as Kristofer stated, but maintenance of preference 
order, which will bring the vote *closer* to being a more accurate 
representation of the voter's actual raw utilities, normalized. It 
doesn't cause the voter to "exaggerate;" that motive comes from 
approval strategy. Want to balance this? Lower resolution range 
increases the cost of maintaining preference. At Range 2, the cost is 
high: one-half vote. Probably too high.

Bucklin has no cost to maintaining preference, so preference will be 
maintained: if we allow equal ranking, it won't be used unless the 
voters actually have no significant preference between the candidates.

(There is a potential Range method which the fractional vote analogy 
to Bucklin, where there is a voting power cost to lowering the rank 
of a candidate. This was actually done in Oklahoma, except they 
didn't allow multiple votes in the top two ranks.  So a Range/Bucklin 
would be counted in rounds, where the top rating is counted, then the 
next, then the next, continuing until a majority of ballots have been 
found to contain a vote for the winner, or all votes have been 
counted, in which case -- if there is a plurality rule -- the 
candidate with the most votes wins.)

>  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.

It was purely a theoretical concept: Borda becomes Range if there are 
many candidates, across the spectrum. That is not a reasonable assumption.

However, Borda with equal ranking allowed (with empty ranks 
resulting) is clearly a pure Range method. We can then see that any 
argument that Borda is superior to Range must mean that the analyst 
thinks the voters must be constrained. ("The method is for honest 
men.... and we are going to make sure by not allowing them to be 
dishonest." Surely there is some kind of weird thinking here!

(The analysis was for sincere voting only, so, unless the voters 
preferred nobodies, a shot in the dark, to the opponent, the voting 
pattern shown wouldn't happen. Absolutely, that's the vulnerability 
of Borda; with Range, what we'd get, with strategy that is just as 
strong but which is actually sincere, in that no expressed 
preferences are false, is favorite > opponent = nobodies, at the extreme.)

>>>>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?

No. I should have stated that the utilities are normalized. Now, 
strictly, Relative Utilitarianism normalizes over a complete, 
universal candidate set, and I don't know how this translates to a 
limited-set election. (It works if the set of candidates on the 
ballot are the possible universe.)

The vNM utilities, I've been assuming are normalized to the set of 
candidates the voter considers reasonably possible. That would be all 
candidates on the ballot, plus any write-ins that the voter considers 
reasonable to include. (A "reasonable" write-in, if the voter 
considers the candidacy impossible, simply gets the same utility as 
the nearest candidate who *is* considered reasonable. Because the 
theoretical probability of election is never zero, there is always a 
finite gap maintained. Pure vNM utilities, if I'm correct, do 
maintain preference order.

>>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...

Here is the kicker: Suppose I want to coerce (or buy) your vote. I 
simply say to you, I have insider access to the ballots.  I want you 
to write in so-and-so. If you don't, bad consequences.

Tell me, does it matter if the coercer can actually see the ballots? 
The above method should work now; in theory it should work even 
without ballot access, but, in fact, clerks don't report isolated 
write-in votes. (So sue them!)

I'm not actually proposing fine-grained Range for public use. I'm not 
really proposing Range at all, immediately. Just Open Voting and 
American Preferential Voting, er, Bucklin.

>>>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".

In Bucklin, all ranked candidates are considered "approved," but the 
approvals are phased in to allow detection of a higher ranked 
majority preference.

>>>>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).

I've made the point many times about STV; the errors of the method 
are confined to the point where eliminations begin. Multiwinner STV 
is *much* better than IRV, the more winners the better it is. 
*However* Asset is just about perfect, and is simpler to vote. (It 
was, and could remain, STV; but if used for IRV, it makes the method 
into something that could be better than Range.... first preference 
candidates aren't actually "eliminated," unless the lower preference 
is used. Lower preferences, then, may decline somewhat, but with no 
cost to performance -- just more need for further deliberative 
process, which is probably *good*. I.e., the average knowledge of the 
public electors re the candidates is probably higher than that of the 
average knowledge of the voters who voted for them.

>>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.

One of the first Bucklin elections was multiwinner. I just saw it the 
other day. Five winners. I think it was basically plurality-at-large; 
every voter had five votes, and the top five vote-getters won.

I have not researched true PR methods using a Bucklin type ballot. It 
should be possible. I'm not sure that it would be better than 
Proportional Approval Voting or Reweighted Range Voting, but I am 
sure that none of this would equal what Asset could do.

>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.

The quota, in that case, would have to be defined upon the votes 
actually cast! Pretty strange election you've just thought of!

>>>>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.
>If it's Range with restrictions, I don't think it would be Range anymore.

In a sense. It is, however, the same basic "construction." Think of 
it as vote-for-one-rating Range. I'm claiming that it is *useful* to 
think of Borda as a restricted Range method. Or of Range as a Borda 
method with some constraints removed.

The most obvious restraint removed is that equal rating is allowed. 
Then, in parallel to this, empty ratings are allowed. That's all. If 
there are N candidates, Borda is Range (N-1), but voters are not 
allowed to use a rating for more than one candidate, and either all 
ratings are used or the voter loses voting power -- in some proposed 
Borda implementations.

>  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.

Exactly, actually: Oklahoma Bucklin, with no majority found in the 
first rounds, became just that (for up to three ranks; but additional 
votes in third rank were allowed).

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