[Election-Methods] Simple two candidate election

Abd ul-Rahman Lomax abd at lomaxdesign.com
Fri Dec 21 20:10:17 PST 2007

At 01:59 PM 12/20/2007, rob brown wrote:
>My understanding has been that in a simple two candidate election,
>there isn't any need for alternative election methods, and all the
>issues that condorcet/approval/range etc attempt to solve simply
>disappear.  A plain old majority vote is "perfect", as long as there
>really are only two candidates.  There is no conflict between strategy
>vs. sincerity, and there is a single Nash equilibrium -- which is
>simply that everyone picks the candidate they prefer.

Yes. If there are really only two candidates, and a majority of 
voters prefer to elect one of them than to have the election fail. 
Basically, the two candidates, properly, are Yes and No to a motion.

If the two candidates are Ralph and Susan, we start to run into 
problems..... because there is generally a third choice, if we care 
about majority rule: none of the above. In majority elections, with 
proper rules -- such as Robert's Rules, standard, if a voter casts a 
blank ballot, it counts in the denominator of the majority fraction. 
It's a valid vote in that sense. (Robert's Rules of Order Newly 
Revised, p.402, "illegal votes.")

>Is this controversial?

Yes, actually. It's quite easy to construct scenarios for small group 
decisions where it it blatantly obvious that the majority preference 
is the wrong choice, and, in fact, all voters will agree.

There is a confusion between the majority criterion and majority 
rule. The majority may decide, by majority vote -- which in its 
purest form must be on a Yes/No motion -- to choose other than the 
first preference of the majority, and small groups *often* do this. 
They do it, in particular, where there is a strong preference of a 
minority vs a weak preference of a majority.

I call my standard example the "pizza election." Three friends want 
to choose a pizza. They are voting methods enthusiasts, and they have 
noticed that a Range ballot can be used as input for Condorcet 
methods and for Range voting. (The Condorcet method must allow equal 
ranking, which causes no problems).

The candidates are, in this order, Pepperoni, Mushroom, Anchovy.

The votes are:
100, 90, 0
100, 90, 0
0, 100, 50

The Condorcet winner is Pepperoni, and this is the first choice of a 
2/3 majority. However, Mushroom is the Range winner. Critics of Range 
assert this -- without giving a concrete example -- as a flaw in Range.

However, let me put it this way. If this group chooses Pepperoni, it 
is quite probably going to have one less member.

In the implementation of Range that I prefer (and it's the same with 
Approval, but there it requires some first preference marker), I 
would analyze ballots for a Condorcet winner, and if there is 
conflict between the Condorcet winner and the Range winner, I'd hold 
an actual runoff. This makes the method Condorcet compliant, yet such 
runoffs would, in actual practice, be quite rare. My opinion is that 
the Range winner would usually win the runoff, if the votes were 
accurate in the first election, due to preferential turnout. If, 
however, there was a lot of exaggerated voting, it's possible that 
the votes concealed the true preference strengths and that the 
Condorcet winner would prevail.

Small possible cost, but it totally answers the alleged majority 
criterion violation of Approval and Range.

>   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.

>   Assuming at least
>some honest voters, this approach might be able to improve the
>"maximum net tangible utility" ("tangible" meaning we are only
>counting the happiness with the results themselves, and ignoring such
>less-measurable utility such as "feeling of fairness" or "elimination
>of resentment" or "long term satisfaction with the election process

Yes, it can. And it does. However, the situation where the majority 
preference is not also a Range winner is unusual. It's just that when 
it happens, it can bite some people deeply.

If, when the discrepancy arises, the majority has the option of 
refusing to accept loss of its first preference, it can do so. There 
is no fairness problem.

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.

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. 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!

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, and, in particular, if 
there was another candidate who would have beaten the winner in a 
pairwise contest. Ahem. Tideman's results in a series of 87 
elections, where he had individual ballot data, showed that there was 
Condorcet failure in 3. In more than one election out of thirty, with 
"alternative vote," which in the U.S. is called "instant runoff 
voting," there was a loss of the preference of a majority. Not 
*first* preference, but preference in the pairwise contest, where all 
other candidates are set aside.

With ratings methods, such as Range, however, which can allow the 
expression of preference strength, majority criterion failure has 
quite a different meaning. Indeed, the failure, particularly if we 
assume sincere votes, is of the criterion itself, not of the voting method.

Robert's Rules prefers election by repeated balloting, until there is 
a winner by a true majority. It disapproves of preference voting, in 
particular, IRV specifically, and the win by an apparent majority in 
the last round of an IRV may not be a true majority if voters have 
declined to cast a vote for all candidates (but one, ranking last 
place is a No vote for that candidate, but possibly a Yes vote for 
any of the others). RR does tolerate IRV in cases where multiple 
ballots are considered impractical and the possibility of a plurality 
win is tolerated.

>  My own opinion has always been that the (perceived?) fairness of
>"everyone's vote counts the same" outweighs any desire for "maximum
>net tangible utility."  I'd even go so far as to say that this would
>be true even if we knew all votes were honest (say we put everyone on
>a perfectly accurate lie detector).

Everyone's vote counts the same. In Approval, consider this: every 
voter has, in the end, cast a vote for the winner or not, and a "not" 
is a vote against the winner. All other votes could be eliminated and 
it would not change the outcome. That is, every voter either casts 
one effective vote or none. The "utility" argument is a red herring. 
It is a method of analysis of election performance.

If we could know that votes were honest -- it's actually not all that 
easy to define -- then Range would, in fact, be an ideal election 
method. Think it would be unfair if your first preference loses 
because you rated an alternative highly, well, then, don't. I'd say 
that an unfair outcome is a poor one, and so that outcome should be rated low.

Approval voting is merely a method of allowing all pairs to be 
considered simultaneously, instead of using sequential dropping as in 
IRV. Approval does select the Condorcet winner, most of the time (I 
think it's higher than with IRV), probably for the same reason that 
Condorcet cycles are quite rare in real elections (one can analyze 
IRV ballots, as Tideman does, to try to find them).

And Range voting? It's really only the *ability* to cast fractional 
votes. Think that it would be unfair if your fractional vote for some 
other candidate hurts your favorite? Don't cast that vote! But 
consider this: in most elections there are two frontrunners, three is 
a rare situation. With two or three, vote for your favorite, and 
against the other one or two. As to other candidates, do what you 
like! I'd recommend a sincere estimate of how happy or unhappy you 
would be with that outcome, but it's highly unlikely to come back and 
bite you. If you were wrong, well, if you voted sincerely, you won't 
be hurt badly.

Simple: Plurality, vote for one. Spoiler effect.
Approval, vote yes or no for each candidate. (same as allowing 
overvoting in Plurality). Spoiler effect almost entirely eliminated.
Range: allows fractional votes, but strategic considerations may lead 
many voters to vote Approval style (and similarly many Approval 
voters, by the nature of elections, will only vote for one).

To express how rare majority criterion failure is likely to be in 
Approval, it requires that many voters vote for both frontrunners. 
Why would they do this? This is the equivalent of voters in 2000 
voting for both Bush and Gore. Yes, there are ballots like that. A 
tiny number. (Currently those ballots are disregarded as overvotes, 
with Approval they would be counted, but these are precisely the 
ballots that could cause the loss of the first preference of a majority.)

Another argument: in states which allow Ballot Questions, if two 
questions both gain a majority, the one that prevails is the one with 
the most Yes votes. This is, precisely, Approval Voting, it is 
standard practice, and I've never seen it asserted that it violates 
basic principles of democracy. Quite the opposite!

>So, I am quite happy with plain old majority vote for a two candidate

So am I, if we want quick and simple. However, important: full debate 
and wide understanding of the impact of the result.

I would not be worried about election methods, though, if we were 
confining ourselves to two choices. If this is a officer election, 
though, what about write-ins? How can you have a "two candidate 
election" in that case?

>   But I am encountering those who seem to disagree with this,
>and who don't seem to have the same concept of "fairness" as I do.
>I'm curious if people here see this as a legitimately controversial

Rob, let me break it to you: I think you hadn't considered this 
matter as deeply as might now be possible for you. There are traps in 
the way we think, resulting from centuries of looking at elections in 
a certain way, they are normal and natural. And misleading.

I certainly hope that you wouldn't insist on that Pepperoni pizza, 
riding roughshod over the Jewish friend. Do I suggest that people use 
Range Voting to make pizza choices? Well, if they have to do it by 
ballot, yes. Usually, they can accomplish even better by simply 
talking about it. Consensus process works in small groups, if the 
society is functional. Does consensus process violate fairness?

It can, if consensus is enforced, i.e., if there is a presumption of 
some status quo that is binding. Otherwise, who are we to say that an 
outcome is unfair that all have agreed to?

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