Head to Head Comparison of Election Methods

[Bart Ingles]

Ron Tannenwald wrote:
> [snip]  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.


In general, it is not possible to tell how the voters would have voted
under Approval from looking at a ranked example.  You need information
about the strength of the voters' preferences.  The result above could
have come from either of the two rated scenarios:

Scenario I:

      Rating:
      100    80    60    40    20    0
      ----------------------------------
20%    A B                           C
20%    A C                           B
39%    B                             AC
21%    C                             AB


Scenario II:

      Rating:
      100    80    60    40    20    0
      ----------------------------------
20%    A                          B  C
20%    A                          C  B
39%    B                             AC
21%    C                             AB

In the first instance, A would get 40% approval, C would recieve close
to 41%, and B somewhere between 42 and 59%.

In the second case, the A voters would cooperate by truncating.  The
Approval vote would be the same as a Plurality vote (or most other
methods).

This assumes the only tactical voting in the ranked example was
truncation.



>    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
> 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.

That last statement is true of any method, given the right
circumstances.  At least under Approval there is never a reason not to
include a vote for your first choice.


>  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)


The concept of Majority may not be as solid as it appears.  Under
Plurality, a "first-choice majority" can include tactical votes from
voters who actually preferred someone else.  This is also true of
Instant Runoff and Bucklin.  I think the Condorcet methods escape this,
but I disagree with this class of methods for other reasons.

Altering Blake's Bucklin example slightly:

30   D R F
15   D F R
11   F R D
44   R D F

The first round ends with 45-D, 11-F, 44-R
The second round ends with 89-D, 75-R, and 26-F.

Knowing this, the F voters should use the tactic of voting for R, then
F:

30   D R F
15   D F R
11   R F D
44   R D F

Now R has 55 first-choice votes.  Is this the real majority, or is one
of the 89-D and 75-R votes in the sincere example the real majority?

Regards,
Bart Ingles




>     2.The winner must have the approval of a majority of voters.
> 
>     3.The method should be simple to explain,understand,and implement.
> 
>    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.
> 
>        Respectfully,
> .
> 
> Ronald Tannenwald
> Chairperson, Mathematics Department
> UMass Dartmouth
> North Dartmouth MA, 02747
> (508) 999-8746
> Fax: 508-910-6917