[EM] Hybrid Beats-All/Approval v. Straight Approval

Forest Simmons fsimmons at pcc.edu
Mon Oct 22 16:20:31 PDT 2001

Hi, congrats on your hiking and climbing exploits.

On Sun, 21 Oct 2001, Joe Weinstein wrote:

> Hybrid Beats-All/Approval  v.  Straight Approval.
> Forest Simmons has asked (Archive message 8222, 'Re: two bit ratings', 11 
> Oct 2001) whether the public might be easier persuaded to go with a hybrid 
> method - Beats-All/Approval - rather than straight Approval.  In the hybrid 
> method, the Beats-All candidate wins if such candidate exists, and otherwise 
> the Approval winner wins.
> I don't know about the public, but for me straight Approval is clearly 
> superior in result, as well as appealingly simpler to describe.  For 
> instance, consider just the following simple examples involving two, three 
> or four candidates.  (Apologies if these examples unwittingly resemble 
> others posted lately to this list.)
> Each line describes a voter bloc:  the left-hand number is the percentage of 
> voters in the bloc, >> divides approved candidates from non-approved 
> candidates, and a notation X=Y signifies that within the given bloc equal 
> numbers of voters take X>Y and Y>X.
> Example 1.
> 	55   B>A >>
> 	45   A >> B
> Example 2.
> 	55   B>A >> C
> 	45   A>C >> B

Rob LeGrand would argue that if A won the election, the larger faction
would regret that they voted their sincere approval of A.

To me it seems harmless that a lack of information about the preferences
of fellow voters resulted in a winner sincerely approved by all (in this

However (in defense of Rob's point of view) it seems to me that if a
method yields results that make people regret sincere voting, then voters
can be manipulated by mis-information into an unsatisfactory result.

If voters are satisfied (after the fact) with their sincere vote (i.e.
they wouldn't change it if the election were repeated) then their vote is
less likely to be manipulated by mis-information.

I believe that the candidate with the greatest sincere approval is the one
most likely to serve the best interests of the electorate as a whole.

Furthermore, under Approval, when votes are not sincere, they tend to be
bent towards the beats-all winner, as long as horse race style polls are
accurate. That's OK, it just saves us the trouble of inserting a beats all
feature into our method.

I'm still worried about the case when poll information is inaccurate for
whatever reasons.

Suppose, for example that sincere ballots would have been ...

55 B >> A > C
45 A > C >> B

but the polls are falsified to say that neither B nor A has much of a
chance ... that C is way out in front. 

Then it would be natural for the first faction to graduate A to approved
status. Then A would be the Approval winner, even though B was both the
sincere approval candidate and the CW.

As I see it, checking for a beats all winner (and saving the approval
winner for tie breaker) relieves some of the stress associated with
strategic voting (i.e. the worry that you may be basing your strategy on
inaccurate horse race information).

> Example 3.
> 	12   B>A >> C1=C2
> 	08   A >> C1=C2>B
> 	20   C1 >> B>C2>A
> 	20   C1>A >>B> C2
> 	20   C2 >> B>C1>A
> 	20   C2>A >> B>C1

I like your Example 3 showing that the beats all loser (i.e. reverse
beats all winner) can be the Approval winner even when there are four

Someday, someone with a lot of time on his/her hands should dig through
these archives and publish all of the good examples and counter examples
in a book like the classic book of examples and counterexamples in

As you noted, there is a lot of room for improvement in the literature of
election methods.


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