Head to Head Comparison of Election Methods

[Blake Cretney]

Ron Tannenwald wrote:

>   I think Dumais' method is very interesting and has many virtues,but
> simplicity
> is not one of them.I fully agree that the "winner" should have majority
> approval
> from the electorate.It is assumed that ballot truncation is a strategic
> ploy and
> that the voter has no preference among the candidates omitted,hence the
> remaining points are distributed equally.But ballot truncation may be the
> voter's way of expressing disapproval of those truncated.Assume,for a
moment,
> this to be the case and consider the following example:
> 
> 
>       20%      20%     39%    21%
>       ---      ---     ---    ---
> 
>        A        A       B      C
>        B        C
>        C        B
> 
>    Most of the familiar methods (Plurality,Instant Runoff,Condorcet ,and
> Dumais)
> would declare A the victor. Candidate A has only 40% approval. Candidate B
has
> nearly the number of first place tallies,79% approval, and is the first or
> second choice of 59%.If a winner is to be annointed I think it should be B.

I notice that by your definition, a vote of 
A C B
gives approval to B, but one of
A C
does not.  Is this intentional?

I think you may be reading more into ranked votes than is really
possible.  I personally may disprove of many, if not all, of the
candidates running, but I would still rank them unless I truly had no
preference, or the method encouraged short rankings.

> 
>    I am NOT a fan of Approval Voting.It was first proposed in the decade
after
> Arrow's famous result appeared.It is simple (to understand and implement)
and
> technically is independent of irrelevant alternatives which seems to set it
> apart from all ranking methods.Its main proponent Professor Steven Brams of
> NYU

Of course, technically, plurality is also immune to irrelevant
alternatives.  This criterion really only makes sense for ranked
ballots, which is what Arrow was discussing.

> writes research articles which purport to mathematically prove its
superiority
> under the assumption that voter's feelings about candidates are
> dichotomous. This hypothesis is preposterous! No voter's attitudes about
> candidates are dichotomous.I would approve of Prof. Brams in a two-way race
> against an Adolf
> Hitler and not approve of him in a two-way contest against an Honest Abe
> Lincoln. Furthermore,if my favored candidate withdrew from the race I might
> very
> well change my non-approval of another to approval;so,in actuality,this
> method is not independent of irrelevant alternatives.Approval Voting
> violates
> the majority criterion (sometimes dramatically).To overcome this major
> shortcoming voters are forced to employ strategies that hide their true
> feelings.Simplicity is about the only thing in its favor(but Plurality
> Voting is
> even simpler.)
> 
>      To justify my choice of a voting procedure let me set forth some
criteria
> I feel are necessities.
> 
>     1.Majority Criteria (i.e. if a candidate is the first choice of a
majority,
>                           that candidate wins)
> 
>     2.The winner must have the approval of a majority of voters.
> 

What do you mean by this?  Do you mean that the winner must be
preferred by a majority to the option of having a new election?  

> 
>     3.The method should be simple to explain,understand,and implement.

Certainly, simplicity is desirable.  On the other hand, no one can
claim that STV is simple, but people still seem to be able to use it. 
Voter's don't necessarily need to know exactly how a method works, as
long as they have a general idea.  Many Americans probably don't
really understand the electoral college, but they can still vote for
President.  How many could explain the procedure used when no
candidate wins a majority of electoral votes?

I tend to view single-winner election methods as primarily useful for
parliaments and legislatures, as well as clubs and other
organizations.  Presumably a more complicated method could be used in
this setting than in a general election, where I favour some form of
PR.

>    With the understanding that no method is ideal,my preference would be
> Bucklin voting with the proviso that should no candidate receive majority
> approval the election is void and no present candidate can run in the new
> election.
> 
>     Bucklin voting is certainly simple and has been used
> historically;voters immediately saw that their lower choices might hurt
> their favorites(a property common to most ranking systems without
> elimination, but not so obvious) and so many voted bullets.The second part
> of my scheme is meant to discourage strategic
> truncation of ballots.Voters do so now at their peril.

There's an important distinction here.  In many methods, including
Borda and most Condorcet completion methods, lower votes can both hurt
and help higher candidates.  There is no justification for deciding as
a general rule to bullet vote, although bullet voting may be useful
for some voters in particular situations.

That's rather different from Bucklin, where bullet voting helps your
favourite candidate, in general.  In fact, it can often help, but
never hurt your favourite candidate.

Consider an election held under Bucklin, with three candidates.  I'm
going to call these Democrat, Republican, and Fringe.

Sincere votes might very well be like this

45 D R F
11 F R D
44 R D F

That is, it is quite reasonable to expect that often main-stream
voters will prefer each other's candidate to that of the fringe.

In this example, the Republican wins.  If however, the Democrats
truncated, the Democrat would win.  This is because most of the
Republican's second choice support is coming from Democrats. 
Likewise, if the Republicans truncated, their candidate would be back
in a winning position.  The election might well be decided based on
which side can convince more of their supporters to bullet vote, or
under your suggestion, which side is less afraid to trigger a new
election.

So, it is little suprise that the vast majority of voters truncated. 
Not that this is such a bad thing.  There is no reason for the Fringe
voters to truncate, so the winner will likely be the Condorcet winner,
at least in this example.  However, the major parties will still be
able to use the argument that 90% of people truncate to try to get the
reform repealed.  A more serious problem would be if one side used
bullet voting more than the other did.

My major problem with Bucklin is demonstrated in the following
example

45 D R F
11 F R D
44 R D F

Remember that R won before.  Now imagine that the Democrats ran two
candidates.

45 D1 D2 R F
11 F R D1 D2
44 R D1 D2 F

I have ranked both the same with respect to the other candidates.  In
this example, D1 wins easily.  This is because if people vote along
party lines, the more candidates a party runs, the further down the
vote will have to go before it switches to an opposing party.  It
would not be surprising if the ballot got very long indeed under this
rule.

My other problem with Bucklin voting is that it doesn't meet the
Condorcet Criterion.  This results in it behaving oddly in certain
circumstances.  Consider a vote on the conduct of a controversial club
president.  There are the range of alternate resolutions before the
club members:

A-  Bill Smith should be commended for his work as club president,
and his work should be memorialized with a plaque.
B-  Bill Smith should be commended for his work as club president,
but no plaque.
C-  No Action.
D-  Bill Smith should be condemned for his incompetence as club
president.

Now, imagine that the votes are as follows.  Note that these are all
logical in this obviously linear example.

40 B A C D
21 C B A D
39 D C B A

Under Bucklin, B would win.  Commendation.

But imagine that Bill had not annoyed so many people.  Imagine that
the preferences of the D voters slid to the more favourable C action. 
The result could be

40 B A C D
21 C B A D
39 C D B A

So, the generally more favourable attitude towards Bill costs him his
commendation.  To me, this is a very odd effect.  It is even more
pronounced in IRV and plurality.  However, any Condorcet method has
the advantage that if some voters slide one way on a linear question,
the method's winner will not slide the other.

---

Blake Cretney