# [Election-Methods] Simple two candidate election

rob brown rob at karmatics.com
Fri Dec 21 22:32:10 PST 2007

```On Dec 21, 2007 8:10 PM, Abd ul-Rahman Lomax <abd at lomaxdesign.com> wrote:

> 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
>
> >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.
>

Your example is for more than two candidates.  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.
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.

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.

> 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.
>
> 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.

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.

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.
>

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.

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

> >   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
> >itself").
>
> 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.
>

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.

> 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?

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

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.

> 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.  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.

-rob
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