[EM] The worst about each system; Approval Preferential

[Abd ul-Rahman Lomax]

At 03:14 AM 5/27/2010, Jameson Quinn wrote:

>2010/5/27 Abd ul-Rahman Lomax 
><<mailto:abd at lomaxdesign.com>abd at lomaxdesign.com>
>At 12:31 AM 5/27/2010, Jameson Quinn wrote:
>As Abd already said, you can avoid the runoff if only one candidate 
>has a majority. Abd's Bucklin proposal tricks many voters into 
>extending more approvals to decrease the chances of a runoff.
>
>I should have been more precise. I believe that with Bucklin/Runoff, 
>people will honestly rank more candidates than are approved with 
>approval/runoff.

Yes, and there are two reasons. The most common immediate objection 
to Approval is that it does not allow the expression of preference 
within the approved class. That can be very important to me as a 
voter. If I'm a Nader supporter in 2000, I want to, at the same time, 
make it clear that I prefer Nader, while allowing my vote to count 
against Bush, i.e., to support Gore. (If I believe Nader's argument 
about Tweedle-Dum and Tweedle-Dee, I may not care.) While Approval 
gives me a better option than Plurality, where it is all-or-nothing, 
it's still unsatisfactory. In addition, there is a minor problem with 
multiple majorities due to over-eager additional approvals, which 
then creates pressure to, next election, bullet vote. It seems fairly 
clear that approval compared to Plurality will not harm results, 
long-term, but will improve them to a degree, and Approval is a 
basically no-cost reform, it would normally require only the removal 
of a line from the election code that requires discarding and not 
considering overvotes.

This applies to approval/runoff as well. If there is no multiple 
majority, it's moot, though some may be upset if they would have 
preferred a runoff to the election of their second favorite, whom 
they additionally approved. They made that approval, presumably, 
because they wanted to make sure that a different candidate was not elected.

So, Bucklin. Bucklin is *similar* to Approval, in practice, but the 
phased approval it sets up allows the expression of that preference, 
and it is even possible, with original Duluth Bucklin, to show 
strong, weak, or  preference. I.e., if it happens to be three 
candidates plus write-in,

>This will help avoid some unnecessary runoffs, which is a good 
>thing. It will also possibly improve the utility of the result for 
>society. However, it is a strategic mistake on their part.

Sure that depends on their preferences and preference strengths. It 
seems that Mr. Quinn is making some possibly unwarranted assumptions here.

>Thus, I call it a "trick"; if they fully understood the situation, 
>they probably would just vote strategically.

With this, I vigorously disagree. While it is possible that some 
voters will "misunderstand" the situation, with good ballot 
instructinons and general education, few are likely to truly 
misunderstand. It is a fact that with high knowledge (hindsight is 
high knowledge!) and with nearly any voting system, a voter may see a 
strategic vote to cast that will improve the outcome for the voter. 
Far more likely, though, is that the voter will see that their vote 
was moot, that they could have stayed home with no change in outcome.

Bucklin is very similar to Approval, and what a "strategic vote" is 
in Bucklin, as in Approval, depends on who the frontrunners are and 
what the preference strengths of the voters are. In Bucklin/runoff, 
there is an additional factor, the possible desire to avoid a runoff 
election. Or, to the contrary, the desire to postpone an approval 
until the runoff. Mr. Quinn seems to assume that if the voter 
understands the situation, the voter will therefore prefer a runoff 
to making an additional approval. But I'd want to see voter education 
on this be very clear: if you would prefer a runoff to the election 
of a candidate, don't approve the candidate!

If you hate runoffs -- some have expressed that opinion here -- then, 
TANSTAAFL, you rationally will take a chance on making a significant 
approval. If you prefer runoffs, you will only add additional 
approvals if you have relatively low preference strength, or, 
alternatively, prefer a no-hope candidate, and you want to help get 
your favored frontrunner into the runoff. With some variations I've 
proposed, you can do both: avoid electing your preferred frontrunner 
in the primary, but help get that candidate into the runoff (by using 
an elevated unapproved class assignment, indicating both preference 
for condorcet analysis, and higher utility.)

The basic instructions to the voters are quite simple, as I've 
outlined them, and runoff complicates Bucklin strategy only a little. 
Runoff/Bucklin will almost certainly depress approvals to some 
degree, but what it will depress is holding-my-nose-and-voting for 
the preferred frontrunner. It will not depress genuine additional 
approvals with low preference strength between that candidate and the favorite.

Straight Bucklin without runoff will force voters who want to 
participate in the real election to make a more difficult decision, 
for it's now or never, for them to express approval for other than 
their favorite.

With good rules and education, the set of voters who will feel 
"tricked" when they see the result will be small or empty. Indeed, my 
suspicion is that early Bucklin elections saw overenthusiastic 
additional approvals, and it is possible that later elections saw 
depressed usage of additional approvals. In later party primaries, 
the report is that additional approvals ran as low as 11% or so. 
That's not a bad figure! Whether it shows a problem or not depends on 
context and the nature of the candidates in the election. I rather 
dislike party primaries as deterministic methods, I'd much rather see 
a simple range poll, with the actual nomination decision made by 
majority vote at a party nomination convention, and with a good 
system of representation of party membership that's easy for party 
members to participate in. I'd prefer to see a better definition of 
"party membership" than simple declaration. Talk about 
turkey-raising! But it isn't necessarily a simple problem.

If public campaign financing were made available to a party through 
registration as a party member, and that registration determined 
eligibility to vote on representation at the convention, that would 
set up a natural barrier to turkey-raising through false 
registration. Fine. You want to vote for "turkey," provide the party 
with campaign funding! But you'll probably be wasting your efforts....

>Being a trick doesn't make it evil; on the contrary, if anything, it 
>helps the social utility.

If it's open and it improves overall utility, even calling it a trick 
is unwarranted. It's a device, and I designed this specifically as a 
device to encourage sincere Range voting, with an event to hang 
commensurability on: the utility of a runoff election. This is 
exactly the incentive for compromise that exists in the fundamental 
and standard repeat ballot method of election (majority required). 
Indeed, the only differences between this and repeated ballot are (1) 
use of a more efficient system for discovery of majority than 
vote-for-one, (2) handling of a multiple majority possibility, which 
does not arise with repeated plurality ballot, and (3) a 
deterministic runoff election, but not one which "guarantees" a 
majority by restricting the candidates to two, necessarily. That 
"guaranteed majority" is false, because of the exclusion of options. 
If write-in votes are allowed in the runoff, and with a good runoff 
method there is no necessity to prohibit them -- the default in 
California is that they are allowed -- there is no true exclusion, 
merely a depression, under some or most conditions, of the relevance 
of a write-in campaign.

Normally, runoff/Bucklin, even with the triple candidate possibility, 
would only have two ballot candidates, allowing the improved 
examination of candidates that is a notable feature of runoff elections.

>But it does make it unstable; people might see through it, and it 
>would stop working.

The error here is in assuming that such unwise votes are essential to 
it "working." Look, think it through. If everyone bullet votes, 
period, the method, no matter how sophisticated, has reduced, in the 
primary at least, to top-two runoff. And this method is proposed to 
replace top-two runoff at low cost. To be an improvement, it only has 
to save a few runoffs. I submit that in most situations, it will save 
much more than that. It's speculative and it depends on the local 
conditions and the number of candidates, but I'd expect to see 
something like two-thirds of runoffs eliminated.

But there is a contrary force: good voting systems encourage 
additional candidacies! San Francisco has 23 candidates in some 
single-seat supervisorial elections because they had top-two runoff 
and then IRV. Is that a good thing or a bad thing? Probably, my 
guess, is that it's good for the district. There is another purpose 
besides election being served: vetting candidates for the *next* 
election. And increasing a sense of community participation. 
Providing a better primary method (or even a better deterministic 
election method) will preserve that, allowing voters to express true 
preference, while still finding the optimal candidate from the 
expressed preferences and preference strengths.

When there are many candidates, it's difficult for voters to discover 
and remember less-preferred candidates. Deep ranking is probably 
collecting, mostly, noise. A runoff election between the best 
possible candidates, as shown in the primary, allows the voters to 
get a second look, this time with more media attention more narrowly 
focused. Normally that would just be two candidates, but, because of 
various considerations, it's possible that the best candidate, 
overall, would be third by some measure, such as first-preference 
votes, and examples have been shown many times. A centrist, for 
example, can easily be third in first preference, but beat the other, 
supposedly-more-preferred candidates, by two to one. That's rational 
from any linear arrangement of voters and candidates on a spectrum, 
if the three "parties" are equally distributed.

>(If they have a rational degree of doubt in their own judgement of 
>which option is best, and are voting altruistically, and believe 
>that a majority of voters are voting altruistically or have no 
>negative-sum interests at stake, then it's not a mistake, but the 
>first part at least clearly doesn't describe most.)

>Most voters, generally, have little doubt about their first 
>preference, but those who do are not a small number, just not the 
>majority. These are voters who, in fact, are very likely to add 
>additional approvals, since they had difficulty deciding which is 
>preferred in the first place. They are voters who, if they prefer 
>A>B>?, would vote, in 3-rank Bucklin, A>B>? vs A>.>B?. (? depends on 
>the existence of a third, less preferred but still approved 
>candidate, ?.? indicates an empty Bucklin rank, the additional 
>approval is not counted until the third round.


What I see is that some voters may, initially, over-approve, but that 
this will naturally settle, and it will do little or no harm in the 
interim. As a runoff method, it is designed to handle truncation.

But, consider: if you prefer A>B>C, and you are relatively close to 
B, such that you have relatively low preference strength for A over 
B, but high strength for A over C and relatively high for B over C, 
you have a strong incentive to give a third rank approval, at least, 
to B. Are you going to be upset if B wins? I don't think so, I think 
you will be pleased, while, at the same time, you have expressed your 
preference for A. If that vote shows that the A faction is stronger 
than the C faction, your faction will have more influence over B, 
probably, and you will be in a better position for the next election. 
If the vote shows that without your additional approval, the runoff 
would have been between B and C, your will see your vote for B as at 
least harmless, and possibly quite helpful, particularly if that 
approval took B up to creating a runoff in some way.

When would you regret the vote? You wouldn't ever have *much* regret, 
by the description of the situation. But if, say, there is a multiple 
majority for A and B, whereas without the vote A would have won, 
you'd have some possible regret. But if this is runoff and multiple 
majorities trigger a runoff, you'd have no serious regret, you'd 
still be able to vote for A over B. In the end, if B wins, it will be 
because, *clearly*, the electorate prefers B. People don't have much 
problem with that, they won't blame the election method! They may 
blame the majority for its stupidity, but that's a completely different issue!

>In APV, adding additional preferences (beyond the approval ballot) 
>is not a strategic mistake, which I think makes it more robust. It 
>also still has the same justifications in human psychology.
>
>Correct strategy in APV when the two frontrunners are ideologically 
>distinct is to disapprove one and everybody worse, prefer the other 
>and everybody better, and approve everybody in between.

Eh? That forces favorite betrayal, doesn't it? "Correct strategy" 
presumes that a particular goal is "correct." What is it, in this 
case? Presumed here is an assumption that ideology is the issue. How 
about competence? Character? Ability to compromise? Being your 
father-in-law? Voters have complex motivations. In utility analysis, 
we assume that preferences are on a scale, and this scale is 
generally "linearized" and then, for an election situation, 
"normalized" to the possible candidate set. The linearization is 
intrinsic, basically, whatever adjustment makes a preference step at 
one part of the scale equivalent to one step at another part, is 
assumed. To make this model correspond to real preferences could be 
the object of research all on its own...

Normalization, though, causes real error in amalgamating utilities. 
It's hoped that this error will average out, but that could be a 
false hope. Which is why I believe that range results should always 
be ratified, when possible, in the situation where a utility winner 
beats a more popular winner. Utility advocates fear that the majority 
will simply stomp on the minority, but that flies in the face of the 
nature of the situation which creates this anomaly: low preference 
strength for the preferred candidate. Otherwise these two winners 
will be the same.

Given this, to get good results from Range requires that voters have 
the means and opportunity to express good, sincere preferences and 
preference strength. The Bucklin system I've described, besides being 
very similar to what was already used (Bucklin, 1910-1920 and 
beyond), or is in wide use (Runoff voting, which was long considered 
a major reform), appears to strategically encourage sincere Range 
voting. That alone makes it worthy of attention. The flaw in Mr. 
Quinn's argument is that he believes the "strategic vote" is 
necessarily the bullet vote. That, we have amply shown in many 
situations, is not true. It depends on preferences and preference 
strengths, as well as an assessment of election probabilities. These 
are all components of individual decision-making, and of 
high-performing collective decision-making.

This brings together political theory and utility theory (which was 
mostly used in economics).

>  If they're near-clones ideologically (ie, near to same value for 
> most people who aren't strong supporters of one of them), then do 
> the same using the third frontrunner and the most-distinct of the 
> first two; that automatically means at least one approval, for the 
> other clonelike frontrunner. Both of these strategies, if widely 
> followed and if the "frontrunner" determination is common 
> knowledge, never lead to a runoff.
>
>Bucklin, very similar to what I'm proposing, was widely used for a 
>time. We know that some voters don't like being restricted to three 
>ranks in RCV. Additional expression, *if voluntary*, is, in my book, 
>a good thing.
>
>If voluntary and honest. But one dishonest strategic expression can 
>"poison" a number of honest expressions. Moreover, even semi-honest 
>strategy creates two classes of voting power - strategic and 
>nonstrategic - which hurts legitimacy.

I would encourage all voters to vote strategically and honestly. In a 
Bucklin system there is no advantage to dishonesty that is worth the 
risk. I.e., from a game theory point of view, net zero or negative 
expected gain.

The *actual strategy* that a voter follows depends on their 
preferences, their preference strengths, and their assessment of 
realistic possibilities. What I believe is that the 
Bucklin/Range/Condorcet runoff systems I've been describing will 
encourage (1) reasonably deep ranking, allowing decent Condorcet 
performance by allowing the necessary preferences to be expressed, 
(2) serious consideration of adding additional approvals; whether or 
not the voter adds additional approvals, to be absolutely maximized, 
would require complex analysis with little, if any, improvement over 
a simple assessment of voter impressions at the time of voting. As 
I've mentioned, it is always true that if the voter has perfect 
knowledge of the remainder of the electorate, there is a bullet vote 
(or, in this system, some possible combination of votes) that would 
be seen as possibly improving the outcome; the improvement could be 
definite if completing an election in a primary is involved, or 
merely possible if the result is to trigger a runoff.) But 
comprehensive knowledge is generally missing, so only *general 
strategies* are available.

The most common is to make sure that one either votes for the favored 
frontrunner, or acts to insure, if it seems necessary, that the 
favored frontrunner is in the runoff. Which choice the voter makes 
will depend on what would be obsessively complex assessments if the 
voter wants to be absolutely maximal. I doubt there is one voter who 
would do the work, figuring out probabilities of each outcome, and 
thus distributing voting power according to von Neumann-Morganstern 
utilities. But the system does allow such utilities to be voted, if 
the voter wants, with decent facility, i.e., if we modify Arrow's 
theorem to only be concerned with the system social choice, single, 
and if we use the Dhillon-Mertens modification of Arrow's criteria to 
allow consideration of utility sum methods (Approval, Range, most 
notably), this method would satisfy those criteria, I believe. It 
does so if it guarantees that, even if they differ, the Approval and 
Range winner (Here, Range is more important, actually) are in the 
runoff, and if one exists, a preference winner (Condorcet winner) is, as well.

Yet the voting system and how to rationally vote it are very simple. 
I've asked this before: why isn't everyone jumping up and down? I'm 
seeing some kind of relucant move toward Bucklin, and all I've been 
proposing are some tweaks to Bucklin that should improve performance, 
or at least do no harm, and I'm proposing using Bucklin as an 
improvement of a runoff system, thus *incorporating* what was, till 
recently, the most popular and long-lasting voting reform, runoff 
voting. FairVote has been trying to tear down runoff voting, instead 
of fixing and improving it, and the idea of using IRV to fix runoff 
voting probably did not occur to them, because of two factors: IRV 
and top two runoff suffer from the very serious problem, not a rare 
occurence when there are three viable candidates or more, of center 
squeeze. And they even called IRV "instant runoff voting" as a device 
to get the STV method implemented, with the idea of making the next 
step to STV-PR not such a big, expensive one.

But the whole strategy was misconceived. There are better and cheaper 
methods of proportional representation, we believe. STV itself can be 
effectively implemented with simple approval ballot, with Asset 
Voting, and there are other possibilities, such as Brams' SAV. (Asset 
would be truly revolutionary, while being very simple for voters and 
*fully* representational).

For single winner elections, the best and most open for further 
improvement method, to improve top two runoff, is Bucklin. Because 
some of the tweaks are so easy and so unlikely to cause harm, I'd 
suggest that at least a few of them be immediatelly used, such as 
allowing equal ranking in all ranks. Quite simply, since sensible 
strategy would only rarely *require* equal ranking, but the method 
would merely *allow* it, and since equal ranking is already allowed 
in original Bucklin in the third rank (and most seriously contested 
elections did go the full three ranks, thus collapsing to pure, 
unconstrained full-on Approval, having passed through the important 
phase of preference expressing within the approved set).

This is important: the math hasn't been done, but my intuition here 
is that the rational strategic Bucklin ballot is a Range ballot with 
these restrictions: the candidates are divided into two sets, 
approved and non-approved, and range ratings are best as sincere 
ratings *within these sets*. The voting method then handles the 
optimal strategy! Some work has been done on sequential approval, 
where voters start out, first ballot, with a first preference 
expression. (And there is no reason to *disallow*  equal ranking on 
the first ballot. It accurately expresses, in this context, 
negligible preference between them). Then, with each ballot, the 
voters, reviewing the voting in the previous ballot, begin to lower 
their approval cutoff, as they see fit. The faster they lower this, 
the speedier the decision, but the risk of the bete noir of approval: 
multiple majorities, caused by too-speedy lowering of the approval 
cutoff, not knowing how other voters will handle the problem.

But when the final result, if not unambiguous, must be ratified in 
some way (as with a runoff election, in effet), that "problem" isn't 
one, there is only the nuisance of a runoff election, if it's 
considered that. Robert's Rules of Order *likes* repeated ballot 
because better compromises can be made (avoiding center squeeze, they 
are explicit about this), and because of improved and narrowed focus, 
and with the voters better understanding what compromises might be necessary.

Range advocates, here is a path to Range Voting that brings in, at 
the beginning, a ballot that is actually a kind of range ballot, and 
with a suggested tweak that makes the method use a full-on Range 
ballot. Further, it can be tweaked to guarantee that the Range winner 
is either elected or gets into the runoff and has a serious chance of 
getting elected. My view is that this is the *best* that we can hope 
for for Range, and that this will actually *improve* utility results 
over simply choosing the Range winner.

It is a more sophisticated version of what Warren called Range+2, top 
two runoff Range, but more efficient and more likely to choose the 
best candidate. The trick to understanding this is that expressed 
preferences are normalized, but turnout is based on absolute 
preference strength. If we want to maximize *actual collective social 
utility,* we need to, in some way, tie expressed preferences to some 
commensurable value. Here, it is avoiding or causing a runoff 
election. The cost of the runoff is two-fold: the actual cost of 
voting and counting the vote, plus the inconvenience to the voters 
(which is probably the largest cost), and the risk of a poorer 
decision from the point of view of the voter. (That's unusual, 
probably, and the system I've proposed goes so far in insuring that 
the best candidate makes it to the runoff, and almost certainly the 
best two, that this might be negligible.)

We should remember that Range+2 had lower Bayesian regret than Range 
alone. Why, is a complex question, but I do know that Warren's 
simulation of Buckldin was badly flawed, by a misunderstanding of how 
the system would work and what *sincere* voting strategy would be, 
much less strategic voting. He did not understand that voters could 
and did skip ranks, or add multiple approvals within a rank (third 
rank in the original, in all ranks in the proposals), making the 
ballot into a Range ballot.

Indeed, if it's a two-rank Bucklin method, the ballot *is* a Range 2 
ballot. Classic Bucklin was Range 3, with rating 1 missing (i.e., 
merged with rating 0.)

>That's why adding levers and knobs to your voting system is 
>dangerous if they can be used strategically with impunity.

I've seen no cogent example of this. In evaluating strategy, I'd 
encourage Mr. Quinn and anyone else to *start* with utilities. 
Utilities drive voting strategy, in reality. Bullet voting, for 
example, shows that the voter has strong preference for the favorite. 
Many analyses of Range voting, for example, have assumed weak 
preference for the favorite, but then some supposed outrage when the 
first preference isn't chosen. That's contradictory! Saari fell into this one.

Voters will bullet vote, commonly. It is a rational and sensible and 
*sincere* strategy, properly understood.

>  I believe that the best solution to expressiveness is not a 
> "kitchen sink" system such as some of Abd's proposals, but a 
> drastically simple system with an official, nonbinding, 
> Range/Condorcet/Bucklin poll attached.

What I'm proposing is very, very close to a system that was already 
in use and that worked. The tweaks are not difficult to understand, 
and the main one (equal ranking), Mr. Quinn already agrees with. We 
both also propose a tweak that will cause the method to become, 
possibly, Condorcet compliant. (The issue will be how many ranks are 
allowed and whether or not this causes suppression of the necessary 
preference votes. It's a complex issue, but if there are as many 
ratings available on the Range ballot feeding the Bucklin/Runoff 
method, that issue should go away.)

Mr. Quinn's proposal is indeed simpler, but almost every Bucklin 
implementation used three ranks. As a result, the method was able to 
handle large numbers of candidates. Three ranks encourages, at least 
a few, additional approvals, thus possibly avoiding a few runoffs. I 
see no down side to allowing three approved ranks, and that, right 
there, allows three ranks for Condorcet analysis. To make this more 
complete from Condorcet perspective, there should be two or three 
disapproved ranks, instead of just one. That's all.

And then the details of how the runoff candidates are chosen are, as 
well, simple and not hard to understand. There are some options for 
"top two" when Condorcet is irrelevant (i.e., the condorcet winner is 
already in the set of other winners). I've suggested some simple 
options, but the simplest, the top two vote getters in approval, is 
not bad. But since we now have what is apparently sincere Range 
ballot data, and sincere Condorcet ranking for up to, say, five 
candidates, with equal ranking still providing a lot of pairwise data 
beyond that, why not use it for this narrow purpose? The result is a 
method which should please Condorcet advocates, since it would only 
deny a condorcet winner through a runoff where that was explicit, 
perhaps (depends on the details of the runoff method). But it should 
also please Approval and Range advocates. And it should please 
election officials, since it would be precinct-summable and, because 
we are only interested in whether or not there is a 
beats-approval/range winner, the Condorcet tweak is not a great burden.

>Voters rank each candidate as preferred, approved, or unapproved.
>
>
>So you have an explicit disapproved rank? How is this treated 
>compared to a blank?
>
>
>Same as blank. Exists only to prevent accidentally approving when 
>trying to vote "against". Tallied together but break-out percentages 
>reported for anyone who cares.

In other words, you are collecting as much data as three-rank 
Bucklin, but merely constraining the expression of the voters to 2 
approved ranks.

>  If any candidates have a majority ranking them at-least-approved, 
> then the one of those which is most preferred wins outright.
>
>
>Right. With quite possibly bizarre outcomes.
>
>
>No more bizarre than closed primaries, at the very worst.

One is getting desperate when one justifies a system as being no 
worse than a bizarre system.

>  That is, a solid majority coalition might elect its more radical 
> member, not the centrist. "Solid majority" means that the median 
> voter is a member of that coalition, supporting the "radical" on 
> that side over all other candidates. Unlike closed primaries, if 
> there's a majority but it's not solid, the centrist from that side 
> is probably elected.

In the example shown, there was a drastic difference between the 
winner and loser. The loser was massively approved, the winner only 
barely. Bare approval in a situation like that is quite likely to be 
an anomaly. But without having a set of utilities to start with, we 
cannot judge a scenario outcome, not well, anyway. If the approvals 
represented sincere approval, the approval winner would *certainly* 
have been the best. Mr. Quinn is arguing that preferring the 
most-preferred candidate will, then encourage additional approvals. 
But then he discards those approvals in this scenario, making them 
useless. Tell me again, exactly why do we want to encourage people 
with a strong preference for first preference to add additional 
approvals? Beyond the natural encouragement of avoiding a runoff -- 
when "strong preference" means they'd rather have a runoff?

>Personally, I don't see that as necessarily bad - think of it as a 
>small taste of time-series proportional representation. In other 
>words, a bit of diversity, instead of centrists winning always, 
>could be healthy.

Sure. But if that's what we are doing, it would be much better for it 
to be explicit. In Alcoholics Anonymous, standard method for electing 
delegates to the World Service Conference is by two-thirds vote. If, 
after what is considered sufficient balloting, and voluntary 
withdrawals, no 2/3 consensus can be found, they determine the 
delegate by lot from the top two. It is explicitly done in order to 
provide a little additional representation, overall, for minority 
views. That's pretty good for a method that was, I think, devised in the 1950s.

>... instead of his 1, 0.75, and 0, it should be 1, 0.5, 0. But that 
>isn't used in this present statement of the method. It's simply Range analysis.
>
>
>This is only for the nonbinding poll. People can set these numbers 
>explicitly, those were just defaults. Actually, the right default 
>value for the "approved" rank is the average of the value people 
>explicitly write in for that rank. I do suspect that people would be 
>more likely to write in values above 0.5 than below it, so I suspect 
>that number will be closer to 0.75 than to 0.5.

You have two approved ranks. Range ballots are always representative 
of a range of actual utilities. If we assume that voters set midrange 
as their approval cutoff, meaning the middle expected outcome, 
approval could mean above this level, or it could mean that the voter 
rounds off to this level. In other words, goes a little below the 
middle, as "close enough."

I'd simply move to an explicit Range ballot if the jurisdiction were 
ready for that. It would still be analyzed as Bucklin for most 
purposes. I'd want to see as many ratings on the ballot as there are 
candidates, probably with rating of zero being implicit, not 
explicit. I won't argue this now, but there are several reasons for 
it, not the least of which that it's traditional. You mark candidates 
that you are, in some way, voting *for*. If we are going to use 
voting *against* as the model, we might want to use a +/1 scale. It's 
possible to set a different default than min-range, but I won't go there now.

If we assume that voters are classifying candidates into three sets, 
i.e., with traditional 3-rank Bucklin, and if we assume that the 
range of preferences involved are *equal*, so that the difference 
from rank to rank is equal, except for (original Bucklin) half the 
ballot range is "unapproved" We would get, for range analysis, the 
middle of each rank range:

0   -  0.25  /
0.25 - 0.5  / unapproved, average across both ranges 0.25 (1/4)
0.5 -  0.75 / approved, average 0.62 (5/8)
0,75 - 1.0  / preferred, average 0.83. (7/8)

Subtracting 1/4 from each, we get ratings of 3/8 and 5/8

Converting to a full vote, this is 0.6 and 1.0

But we could also treat equal ranking top as different from bullet top.

I'd prefer to keep range simpler. In reality what matters is the 
difference between range steps. Each step represents a certain 
strength of preference. There is roundoff error, to be sure. The 
higher the resolution, the less significant it is. The effect of 
simple Range counting is that the members of each rating class are 
treated as if they were all valued at the top of the range in the class.

>
>
>
>  If not, then the two candidates which are most preferred against 
> all others (ie, the two Condorcet winners based on these simple 
> ballots, or the two most-preferred in case of a Condorcet tie) 
> proceed to a runoff
>
>
>Utility theory would not suggest his pair. Utility theory suggests 
>the sum of scores candidates. I only suggest including a Condorcet 
>winner because of conflict between utility theory and democratic 
>majority theory. If a result is to be based on "greater summed 
>good," the majority should accept it.
>
>
>Utility theory only works for a nonbinding poll.

Which is what is involved in determining candidates on a runoff 
ballot, if write-in voting is allowed. Write-in voting means that the 
result of the first poll is *not* binding unless a majority was 
found. A majority of voters, or even, in fact, a plurality in the 
runoff, can nullify it. And they have been known to do just that. 
Candidates not on the ballot can sometimes win an election.

>If you're relying on it working, people will manipulate it, and that 
>manipulation will be arguably biased; that is, one side will 
>arguably be doing it more than the other. (Whether there truly is a 
>bias or not doesn't matter; the mere appearance of bias undermines legitimacy.)

What I have not seen is a manipulation scenario that makes sense *for 
the manipulators*, when risks are considered along with possible 
gain. As I've mentioned, though, it is possible that with full 
knowledge, any voting system can be "manipulated," but, if it is a 
utility-maximizing system, the "damage" is limited to the voting 
power of the manipulating faction. It's, in fact, questionable if it 
is damage at all, and if that faction directly uses its power, it 
would not be bothering with "turkey raising" as Mr. Quinn proposed.

I know that Bucklin *did* work. I have no reason to believe that it 
wouldn't continue to do so. The changes I'm suggesting simply improve 
it to reflect modern voting system theory, they are not drastic.

The "manipulations" as designed would be somewhere between difficult 
to impossible. Mr. Quinn did not show an exact scenario that 
reflected how the method would actually work. Basically, it's 
possible that a faction of voters, speaking roughly, could improve 
results, from their perspective, *a little*, using a complex strategy 
that could backfire, easily. Many theorists have proposed voting 
strategies that were like this. In fact, serious voting strategy, 
that requires voters to vote with reversed preference, seems to be 
quite rare, that we would see it in nonpartisan elections seems 
vanishingly possible, to impossible. The strategist is asking voters 
to state on the ballot what they don't believe.

As I've mentioned before, if my favorite candidate suggested that to 
me, the candidate would no longer be my favorite. Thus promoting a 
turkey-raising strategy, in this context, would be very hazardous. 
And I doubt that voters would do it individually. This is a red herring.

The basic error that Mr. Quinn makes is in assuming that bullet 
voting will be a natural and practically universal strategy. 
Definitely, bullet voting will be common. It's common with IRV where 
it's allowed. It's a sensible, rational strategy for a voter without 
sufficient information to do more than vote for their favorite, and 
Lewis Carroll invented Asset Voting to enfranchise these voters with STV.

Then, to the contrary, he posits some clever, conniving strategy to 
manipulate who gets into the runoff so that results, it's believed, 
will improve. I.e, the faction believes that B, say, is more popular 
than their favorite A, but their favorite could beat C. Notice: B is 
the centrist. If they try to arrange for the runoff to be between A 
and C, they run the risk of electing C, the worst candidate from 
their perspective.

Now, how, exactly, would they do this? To understand if they have a 
rational motivation for doing it, we'd need to posit sincere absolute 
utilities for this group. (To get voters to "lie," requires strong 
*absolute* utility difference).

We know that they don't want to approve C, and Mr. Quinn is proposing 
that the problem is in the Condorcet or Range analysis used to 
determine candidates for the runoff, and to suppress the presence of 
B in the runoff. The only way for them to do this would involve these ratings:

(using a Range 4 ballot, Condorcet analysis will be used.)

A: 4
B: 0
C: 1 <- insincere, a sincere vote might be B, 1, C 0.

We must posit these conditions:

A majority of the electorate prefer B to A, so they fear B will beat 
A in the runoff. Right away, I'd be ashamed to be a member of a group 
that wanted to defeat the will of an actual majority, but, yes, some 
people don't think that way. (I'd prefer to put my effort into 
educating the majority, it's a long-term effort that can pay off, 
whereas a short term election victory, when the electorate isn't 
ready for it, can seriously backfire.)

Enough voters prefer C that the extra votes of this manipulative 
faction could put C into the runoff, but keep A out.

Under the conditions, we must assume that B might gain a majority of 
approvals in the primary. What's the expectation of the rest of the 
electorate? Is there any hope for A? Bucklin isn't vulnerable to 
center squeeze, with sincere votes. This faction apparently believes 
that it can beat C in a runoff. How solid is that idea? To be solid, 
very likely, we have first preference votes for B exceeding those for 
C. The centrists, the supporters of C, will likely be split in the 
runoff between A and C, or may not even vote, if it's an A:C runoff.

So we have first preference leader, lets say, is A, B is second or 
third, C is second or third. But second preference? A is a 
frontrunner, and likely, lets' accept, to win a runoff between A and 
C. So look at the C voters. They fear the election of A, so ... they 
will be relatively highly motivated to add an approval for B. In 
three-rank Bucklin, they may vote C>.>B. (Some will vote C>B, and some just C.)

There is a very good chance that B wins in the primary. Let's assume, 
though, that the faction using this strategy is more radical than C. 
This means that B voters will prefer C to A. So some B voters may 
also add approvals for C. Depending on the balance, if the A voters 
add additional approved rating for C, they risk a win for C, in 
several ways. If they use the elevated disapproved rating, they could 
bring C into the runoff, whereas C might have been excluded, but this 
would only be bringing in C as an additional candidate, not shoving B 
out. They lose, their strategy accomplishes nothing, and the voters 
who voted that way will have it in their mind that their party could 
only win by "cheating." Not the way to build a party!

It is major parties, the leaders, that "cheat," when they can get away with it.

Here is the scenario, under the possible rules I proposed, for the 
rating of 1 to cause C to win the primary.

It happens if the approvals and ratings for top two show B and C both 
getting a majority. If the rules only trigger a runoff if the top 
approval getter is beaten pairwise by the runner-up, that preference 
expressed will be looked at: C>B. If C was top, and there are enough 
C>B votes, C wins. Oops!

Suppose there is a majority for C, none for anyone else. It's 
possible that the unapproved votes would be moot, here. But let's 
assume that we still want to see if there is a condorcet winner. C>B 
might confirm the C victory, whereas B>C might cause a runoff.

I do not see this as a strategy that can be used with "impunity." 
There are risks, both political and practical.

The strategy would be visible in ballot analysis, by the way, because 
votes of C>B for this faction, as described, would be rather obvious 
as insincere. Think Nader>Bush>Gore in this system. Individually, 
sure, but a whole faction voting that way> I'd say, next election, 
even if they prevailed, they'd be, to use the technical term, screwed.

The rest of the electorate would not be helpless. The terms of the 
problem require the A voters to reasonably expect they will beat C. 
If this is a fact, the C voters, as I mentioned, will be motivated to 
head this off, and they do it by voting *sincerely*. We know that the 
B/C combined faction is quite a bit larger than A, probably about 
double the size. It only takes enough multiple approvals to keep B in 
the running to defeat the strategy, and those are sensible, sincere 
approvals. Likewise, I've suggested, the B faction, even though 
reasonably confident, may see some risk from A, and they are 
(centrally) further from A, most likely, than they are from C. They 
may cast additional approvals for C. This situation could bring C up 
to majority approval, with the scenario described above, where the 
insincere ranking of C might even make C win.

We have no evidence at all that anyone, in a system like this, would 
even try it. Probably by the time Condorcet analysis is added, we'd 
have good ballot data, so we could watch how elections go. Combined 
with other information, attempts to gain value by "turkey raising" 
would become visible, those voting patterns would show in the ballot 
analyses, whereas turkey raising in top two runoff is invisbile, 
except for publicity leaking.