[Election-Methods] Simple two candidate election

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sat Dec 22 21:21:05 PST 2007

At 01:32 AM 12/22/2007, rob brown wrote:
>Your example is for more than two candidates.

Well, it might seem that way. But there are really only two choices 
that make any sense. The third pizza type was in there simply to make 
the normalization scores make sense. If it's not there, there is a 
problem, and we will get to that.

>   I am not questioning that when there are more than two 
> candidates, it is a different situation.  But there are plenty of 
> possibilities for there to be an election where there really are 
> only two candidates, and that is what my question was about.

Actually, that situation is rare in true democratic process. When it 
happens, it is artificial, and typically represents a loss of 
democracy, a compromise, which has been made in the name of efficiency.

>   While I appreciate that most elections....at least political 
> elections....may have more than two potential candidates, I was 
> trying to restrict it to a simpler case.

But there is always a third potential option, which is None of the 
above. In true democratic process, at face-to-face meetings, unless 
special rules have been implemented (which Robert's Rules advises 
rather strongly against), there is *never* a two-candidate election 
where there is no third option, which is *no* result. The exception: 
the two "candidates" are Yes or No. And even there a majority can 
create any number of other options.

>Say your pizza voters are going to watch a DVD, and the only choices 
>are the two movies from Netflix that are in the mailbox.  It's 
>really just two candidates sometimes.

But couldn't they decide not to watch a DVD at all? Maybe talk. But, 
sure, if there are only two possibilities.... you then have a *real* 
problem with what is called "normalization error" in the theory of 
Range Voting.

>Of course in a small group there are much different 
>dynamics.  Reciprocity comes into play. People tend to be a lot more 
>altrusitic towards their friends or people they are close to.  I 
>think these issues are quite a bit different in larger elections.

Rob is coming to a major point: the difference between elections in a 
small group and in a large group. However, remember, above, he wants 
to simplify the question. Now, it seems, there may be some desire to 
complicate it. Yes, it gets more complicated in large groups. My own 
work, in fact, is to treat this disease, the isolation and separation 
of people that is the cause of this lack of "altruism." I don't, 
myself, call it altruism: we all benefit from living in a society 
where people care about each other.

However, if we are studying election methods, I would think that the 
study would start with methods that work when people vote sincerely, 
with concern for the public welfare. If a method does not work well 
with people being honest and open and caring, how would we expect it 
to work when under *difficult* conditions?

Obviously, the conditions are not the same, and thus, when applied in 
difficult environments, special considerations may be needed. But, 
remember the basic question here: simple two-candidate election. What 
is the "best" outcome? Can the best outcome be found with a simple 
majority vote on two candidates only?

It's quite clear that the *general* answer is no. Many examples can 
be shown where the majority first preference, if we assume this is 
how the majority votes in this case, is not the best outcome. But 
this, then can raise the question Rob raised, of "fairness." I gave 
the pizza example because fairness, in fact, *requires* that we set 
aside the majority preference. It is not claimed that this would 
*always* be true, but merely that the situations exist and are even 
reasonably common where this is the case. Generally, most people will 
agree to give up a small benefit in favor of a large benefit to 
others. And life can get pretty ugly, pretty fast, when people don't.

I have the right of way, driving down a street, with some level of 
traffic. I see a car coming out of a driveway, seeking to enter the 
street. I could drive on, assuming that *someone* later would let 
this car in, or maybe I don't care at all. Or I could stop and let 
the car in. Small loss to me (and small loss to those behind me, 
maybe -- maybe not, depends -- larger gain to the car needing to enter.

Now, democratic process is necessarily deliberative. Otherwise we 
get, in fact, the "tyranny of the majority," without the majority 
ever realizing what it is doing. If it's three people and that pizza, 
they will surely talk about it, and they won't even vote, they will 
find consensus informally. But what if it is three thousand people, 
with one thousand people feeling just like each of the original 
three? Does the best outcome change?

Whether or not there is a practical way to find that outcome is 
another story. Range Voting is not an ultimate solution, full-on 
consensus process is it. That, allegedly, suffers from serious 
efficiency problems, but ... I look at that as an engineering 
problem, and not a problem that is insoluble.

(I should say that "consensus process," to me, is not "everyone must 
agree." Rather, it's a process which *values* the agreement of 
everyone, and which seeks it. If the group size is large enough, or 
if a small group is unlucky, there may be people who aren't going to 
agree to something satisfactory to the others, no matter how much 
time is spent on it. So how far does the group go?

My own answer is majority rule. The majority decides how much is enough.

But the majority will be likely to make wiser decisions if it is 
informed about the true state of consensus in the group before it 
votes on a binding decision. If I had my druthers, Range polls would 
be very common, but not for making decisions; rather as part of the 
deliberative process, and elections would be by majority vote on the 
question "Shall so-and-so be elected to the office?"

That's a two-choice election, not "Shall we elect A or B," *unless* 
the majority has previously decided that (1) the only legal 
candidates are A and B, and (2) the election must be completed with a 
single ballot. In my view, this decision is not true majority rule 
unless the majority has made those decisions specifically about A and 
B and this particular election. (Can a past majority bind a present one?)

> >   For instance, could a two candidate election
> >be improved by, say, collecting information about how *much* each
> >voter likes or dislikes the candidates in question?
>Yes, absolutely, and it happens routinely in deliberative bodies.
>This is why the procedure is not Motion, Second, Vote! Part of the
>discussion reveals preference strengths, and members change their
>votes in accordance with that.
>Hmm, ok, well, is that really an election or more of a "lets all 
>talk about this and agree to something"?  It seems like all these 
>situations are much more social, non-contentious places which are 
>borderline for even having a vote.

The election is the last step, when a majority agree to the outcome. 
Now, I ask this: why is it that Mr. Brown thinks of public elections 
as something different from "let's all talk about this and agree to something?"

I can suspect this: it is because we have completely lost the sense 
of public decision-making as a cooperative process, as a way that the 
community finds unity and common purpose. Instead, it's a contest, a 
battle, there are winners and losers.

Our political system is both the result of this and the cause of 
this. Simply allowing voters to cast a vote for more than one 
candidate, making Plurality into Approval, is a small step toward 
healing this. I emphasize "small." I don't expect it to cause a huge 
change, just a small one, there are other ways that we can reform the 
system that will be more significant, and, in my view, these require 
no changes in law at all.

>I see what you're getting at, but I just don't think the situations 
>scale to larger numbers of people.

Based on what evidence? Again, my suspicion: Based on massive 
cynicism about public process.

The simulations show Range Voting functions to improve overall 
satisfaction with outcome, even with voters voting strategically. 
(The whole concept of strategic voting in Range and Approval is a bit 
of a red herring, as I've noted many times. A "strategic" vote in 
Range is merely a strong opinion; there is no particular reward for 
the strong expression of a weak opinion (that is, the reward, if the 
expressed opinion is stronger than the supposed "real" one, is, by 
definition, small, and there are risks of exaggerating; the system 
might give you want you allegedly want -- or, more to the point, 
might disregard your vote because, as to the two *real* options left, 
you abstained by, say, rating them both zero.)

Approval was designed to be "strategy-proof," so critics ran a 
linguistic trick on it. There really is no reward, ever, to insincere 
voting in Approval, that is, to preference reversal. Rather, an 
Approval voter will *always* vote selfishly and sincerely, they are 
the same thing in Approval, for an Approval vote has one real 
meaning: I will support *these* candidates, and I will not support 
the rest. What is the strategy that Approval is alleged to be 
vulnerable to? It is to vote for your favorite. And not for some 
other candidate whom you allegedly "approve" of. Look at Tideman! He 
analyzes ranked ballot data and assumes that if a voter has ranked a 
candidate, the voter approves of the candidate, and that's the 
"sincere" vote, then the tactical vote is if the voter can get a 
better result by "burying" the lower-preferred candidates. Thus he 
entirely invents a strategic vulnerability through voters, in fact, 
voting sincerely....

Approval Voting rewards voters who understand the context in which 
they are voting. But it does not harm the voter who simply votes for 
his or her favorite.

An *election method* does not care about scale. That, in fact, is the 
whole point about election methods. All the games that people may 
play, in truth or in imagination, one a large scale can happen on a 
small scale. Two people trying to decide what movie to see? One of 
them could allegedly misrepresent his or her preference strength 
against the favorite of the other. But what this boils down to as a 
problem is that an unjust society is not going to generate just 
decisions through election processes. Those two people have a problem 
that is bigger than the movie decision; if they are husband and wife, 
they are in trouble.

And if they are two hundred million people, half Democrats and half 
Republicans (mostly), they are also in trouble if they will lie in 
the thought that they will improve the outcome. Society breaks down 
when we lie to each other, and, again, no election method is going to fix this.

But what I'm suggesting is that election methods that work when 
people are honest are better election methods, and they won't make 
things *worse*. Approval isn't going to change the outcome in the 
vast majority of elections, not under current conditions.

But it opens the door to better process. Range is even better, for 
obvious reasons; basically, it gathers more information from the 
voter so that overall satisfaction with the result can be optimized. 
Again, what is the problem with scale? Range critics allege that 
Range breaks down due to strategic voting, but, not only do 
simulations not show that, but there is no sound theoretical basis 
for the allegation either. What I've seen essentially depends on 
self-contradictory assumptions; the alleged failure mode is 
bullet-voting *which is the status quo, enforced by regulation*. What 
Approval and Range do is to create an *opportunity* for better 
decisions to be made. And the "sincere" voter is not penalized, for 
only weak preferences will be discounted. If I have a weak 
preference, and I express that, and, as a result, my favorite loses, 
one of two things is true: I won't care, because my expressed 
preference was indeed weak, or I will be upset, in which case *I did 
not express my true preference*.

>It is arguable, though, that there is nothing unfair about simply
>awarding the choice to the Range or Approval winner. In the case of
>Approval, the majority has given an explicit consent to this! But I
>prefer that the consent be to the actual result.
>I don't know, I think its a stretch to say that Approval gives 
>majority consensus.  To me giving "approval" is simply "picking 
>candidates that are better than the other options".  I guess some 
>people interpret "approval" more literally than me.

The word "approval" is a red herring. The election system I was 
talking about was Approval with explicit Favorite indication. That 
is, the ballot is really three-rank: Favorite, Accepted, Disapproved. 
Favorite and Accepted are each one vote. (If the voter votes both 
Favorite and Accepted, it's still one vote, "Approval"). Favorite and 
Accepted votes are then considered as ranked votes and a pairwise 
victory of over the Approval winner is detected, which, if it exists, 
triggers a runoff. (the situation that there are two or more pairwise 
winner would need to be addressed, but I'd expect this to be 
extraordinarily rare. Approval usually chooses the Condorcet winner, 
it's expected.)

Then I was noting that, with Approval, if the winner has a majority 
-- which is a little more likely than with Plurality -- the majority 
has explicitly consented to the election of that candidate. If they 
were not giving that consent, then, I'd ask, why did they vote for 
the candidate? (This is much more obvious if there is a majority 
election requirement, which is why that requirement is actually 
really important, and why IRV when it is sold as a replacement for 
runoff elections, but can then elect with the winner getting votes 
from less than a majority of the ballots, as in recent San Francisco 
elections, is really a problem, a loss of an essential principle of 
democratic process.)

But, yes, it's cleaner if the consent is explicit. Robert's Rules' 
solution is repeated balloting until a candidate gains a majority. 
I'll note that this is a case where Plurality works fine. Approval 
and Range would merely be a little more efficient.

(With Range it is necessary to define an Approval cutoff to 
understand if the winner has majority approval.)

>Sometimes an assumption is made that "extreme" votes must be
>insincere or fanatical. While that is possible, Range and Approval
>never reward *truly* insincere votes; my contention is that if
>someone votes the extremes, they have a reason for it. Critics of
>Range will posit a "sincere" rating of 100 and 90 for two candidates,
>but the voter "strategically" votes 100, 0.
>Are those the only two candidates?  If not, ok.  If so, I don't 
>understand what the numbers are relative to.  All the people that 
>might have run but didn't?

Ask the critics this question.

I was pointing out that this is a preposterous assumption. Anyway, 
here is the example I had in mind, quoted from 

>Consider a range voting election in which 100 voters have the power 
>to assign a score between zero and 99. There are two mediocre 
>candidates. Of the 100 voters, 98 greatly dislike Candidate B, but 
>decide to express their distaste for both candidates by giving one 
>point to Candidate A and none to Candidate B. The remaining two 
>voters prefer Candidate B and are more tactical. They award 99 
>points to Candidate B and 0 points to Candidate A. The election ends 
>with B beating A by a landslide of 198 to 98 despite the fact that 
>fully 98% of voters preferred Candidate A.
>Explanation: This example illustrates how a tactical fringe can 
>overrule a vast majority of voters when the majority votes sincerely 
>and the minority votes tactically. Tactical calculations rise 
>exponentially with the entry of more candidates, at which point 
>winners also do not need to have been any voter's first choice.

This example is a little different from what I wrote, but it shows 
the same thinking. Basically, the A voters decided to cast votes of 
1/100 vote strength. They essentially abstained from the election as 
an expression of "distaste." "The remaining voters prefer Candidate B 
and are more tactical."

It would have been more accurate to say that they were more sane and 
practical. They voted for their favorite and not for the less 
favored. In Range 99, every voter seems to have 99 votes to cast, it 
is really one vote, which they can cast in increments of 1/99. There 
is nothing wrong with the outcome of that election, any more than 
there would be anything wrong with deciding the same election in a 
ranked method because the 98 voters declined to rank A and B and only 
two voters voted for B. That is approximately what the A voters did, 
and they would have no grounds to complain about the outcome in either case.

>To me it only makes sense to scale the values so the least favorite 
>choice is 0 and favorite is 100.

Normally, yes. Normalization, it's called, and it is standard Range 
advice. Vote 100 for your favorite, 0 for the most disliked. But 
then, there is "strategy," i.e., considering the true environment. 
These are votes, not expressions of sentiment, though certainly 
sentiment may be a factor in determining them. The basic strategy is 
to vote 100 for the favorite frontrunner and zero for the 
least-favored frontrunner, then 100 for any candidate preferred to 
the frontrunners and 0 for any candidate more disliked than both the 
frontrunners. And then other candidates can be placed wherever you 
like, for whatever effect you think you might want your vote to have.

>It's preposterous,
>really. Why does the voter do this? Because the voter cares that
>their favorite win. How much do they care? Enough to abstain from all
>other pairwise elections (since it makes no sense to rate a candidate
>zero and then rate a less-preferred candidate above zero. This is an
>abstention from every pairwise contest that does not involve the
>favorite.) That's enough to make it a sincere vote!
>Hmmm.  Not sure where yo are going with this.  Maybe I'm confused 
>because the title of the thread is "simple two candidate election", 
>and it appears we aren't talking about such a thing.

It's a general discussion, specifically applied in some places to the 
2-candidate case. In the two-candidate case, "strategy" would 
obviously indicate voting 100 and 0. However, strategy is not 
everything. It is not uncommon to see people abstain from voting in 
two-candidate elections, and for one basic reason: they have little 
preference between the two. Range in a two-candidate election 
*allows* a voter to abstain, like any other method, but it also 
allows something new: a partial abstention, the casting of fractional 
votes. On a theoretical basis, this should improve election 
satisfaction, but it's totally voluntary. Every voter decides for 
himself or herself whether or not to cast a full-strength vote, and, 
in particular, I'd want to see that every voter knows that not voting 
the extreme ratings for at least one candidate each is casting a weak vote.

It really is as if the voter was handed N votes to cast for each 
candidate in an Approval election. Not casting N votes for any 
candidate, but only casting M votes at most, is an M/N absention.

>Now, if the majority has only a weak preference for its favorite, why
>should the majority feel that something is unfair about another
>candidate, more strongly preferred by others, winning? If it bothers
>them, why didn't they vote against that outcome? Again, there is a
>This contradiction exists so easily because we have for centuries
>thought only about rank, we have neglected preference strength in
>voting methods.
>With ranked ballots, we are quite rightly offended if a candidate
>wins who was not the preference of a majority,
>Not me.  I don't even know what "the preference" means when there is 
>a ranked ballot.  I think the only place "majority" is important is 
>when there are two options.

Yes. Which is an essential problem with elections when the elections 
are not ratified by a majority. That ratification would be a Yes/No 
question. If the answer is No, by a majority, the election fails. 
Which the majority has explicitly decided. Leaving it up to a 
"method" is a problem, but with some methods, consent to the result 
may be implicit, and Approval is one of these. Range requires 
something that is not part of standard Range proposals: an explicit 
Approval cutoff.

>   That's one of the reasons I brought up the "voting for a number" 
> scenario, because it hilights the absurdity of being concerned 
> about majority.  Negotiation and compromise is expected, in my opinion.

No decision which has not been approved by a majority is democratic. 
It's, at best, a compromise, made in the name of efficiency. Electing 
officials is really just like any other decision, in principle.

Now, yes, with two candidates *and a presumption that the election 
must complete*, there is little need for Range Voting; however, 
Approval is still useful. Approval is really Plurality without the 
overvoting restrictions. What's the difference? How could Approval 
make a difference with only two candidates?

Well, if you want to know if a majority of those voting have accepted 
the outcome, Approval is better. With Plurality and two candidates, 
there will be a certain percentage of blank ballots and ballots with 
votes for both candidates. What do those mean?

With Plurality, they are simply disregarded. But with Approval, the 
blank ballots could mean that the voter disapproves of both 
candidates, and the double-vote ballots that the voter approves of 
both. Thus it becomes more possible to determine if there was a true 
majority. At no cost, no complexity, no fuss.

As I've mentioned, we already have standard process for the 
two-candidate case, with a majority vote required for either to win: 
Ballot Questions. When two conflicting ballot questions are presented 
in a single election, and both gain a majority, the one with the most 
Yes votes prevails. There really is no difference between a 
two-question ballot and an election with two candidates, with a 
majority vote required to elect. Two conflicting decisions.

The claim of FairVote that Approval has not been used in public 
electiosn in the U.S. is thus a bit misleading. Technically, it's 
correct, as we might not think of Ballot Questions as "elections," 
but, then again, there is Bucklin Voting, which is "instant runoff 
Approval." Which was pretty widely used for a time, and which 
actually functioned well, my own suspicion is that it was shot down 
precisely because it was working, just as was IRV in Ann Arbor. And, 
for another oddity, FairVote cites a claim that early presidential 
elections were a form of Approval, which is not actually true .... 
but is merely ironic in light of the claim of no prior use.

To the main point here: the Majority Criterion is clearly suboptimal; 
situations exist where *every voter* would agree that a different 
outcome is better than their first preference *once they are informed 
as to the preferences of other voters.* People like to agree, and 
most people, making cooperative decisions, would greatly prefer to 
have a decision that everyone thinks is fair, even if it was not the 
first choice of a majority *as long as that first choice was not a 
strong preference over the consensus one.*

I've participated in one group where the first preference of a 
majority would have had about 70% support over all other options. 
Until it was discussed and an Approval poll was taken, which showed 
maybe 80%  acceptability of that first preference, but 99% 
acceptability of a new alternative. The motion was then made to adopt 
the new alternative, and it passed unanimously. That's right. The 
holdout changed her vote. This was a situation where one member of 
this group had said that the change would be made (it was a 
forty-year tradition, at least) would be "over her dead body." But, 
then again, that was an organization that valued unity.

Now, shouldn't we?

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