# [EM] Losing with 65% in the Approval Vote

DEMOREP1 at aol.com DEMOREP1 at aol.com
Mon May 22 20:44:48 PDT 2000

```research at ijs.co.nz asked me to forward the below to the EM list.  Responses
should be directed to him and the EM list.
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Demorep seems to struck at the Approval Vote.
Mr Ossipoff didn't seem to agree; that the method had been strongly
rejected. So I made up a more convincing example, which is
below. I have no idea if it is original.

PS. For those interested, a derivation of my IFPP, with 3
candidates and 1 winners, is at:
http://www.egroups.com/message/politicians-and-polytopes/11?&start=1

http://www.egroups.com/message/election-methods-list/5395?
> DEMOREP1  <DEMOREP1 at a...>
>Date: Tue May 16, 2000 11:04pm
>Subject: Re: [EM] Participation & SARC
>
>Mr. Ossipoff wrote in part-
...
>----
>D - Another example-
>
> 46 A
>  2 AB
>  2 AC
> 25 BC
> 24 CB
>
> 99 [= total]
>
>Using Approval--
>
> A  50
> B  51  (25 BC versus 24 CB)
> C  51

Here is a better one that is a worst case example of those that aim
to make the margin by which a candidate wrong loses, is maximised.

Candidate A has 65% of the vote and loses in the Approval Vote.

------------------
AB  32
AC  33
BC  18
CB  17
Total = 100
------------------

Approval Vote: A:B:C = 65:67:68, so C wins (65<86 & 67<68) (1 winner).

CANDIDATE A HAS 65% OF THE VOTE AND LOSES, IN THE APPROVAL VOTING
METHOD.

WHICH OF THE TWO, STANDARD BORDA AND APPROVAL, CAN GIVE THE BIGGER
CLEAR SURPLUS beyond 50% To The Clear ?, yet Still It Lose.

* To use "the favorite" idea of Mr Ossipoff, candidate "A" is
*   "the favorite" (yet loses).

Other methods:

STV (Alternative Vote): B and C lose by a large margin.

IFPP 1 winner: Quota = 33.33... Candidates B and C are just under
half of the quota, so the winner by far, is the STV winner.

Condorcet: A:B=65:35, A:C=65:35, hence A wins clearly.

Borda: A:B:C=(2*65):(32+2*18+17):(33+18+2*17) = 130:85:85,
-> A wins by a large margin. However it is not always so near to
IFPP; refer to the example below.

Hypothesis: I guess that as the number of candidates increases,
the Approval Voting method can allow more clearly bad examples, than
Borda can. (I don't know)

>
>A has a first choice majority (and is thus a Condorcet Winner).
>
...

====================================
:
:   From: MIKE OSSIPOFF  <nkklrp at h...>
:   Date: Thu May 18, 2000 12:53pm
:   Subject: Re: Participation & SARC
:
:
:>Mr. Ossipoff wrote--
...
:
:>D- It's nice to be in the New Age math era where all results are
:> predicted.
...
:Anyone you talk to will tell you their prediction that the winner
:of the Presidential election will be either Gore or Bush. Maybe
:so, but maybe that's only true because so many people believe it.
:What if all the people who prefer Nader to Gore actually voted for
:wouldn't be self-fulfilling, with Approval.
...

A bad method ought not be used to elect presidents of the USA.
They don't want or need defective methods.
Would Ross Perot want a badly designed preferential voting method?,
No!.
...

:Mike Ossipoff
:
=============================================

I add this to suggest that Borda is hardly better.

The similarity of this example adverse to Borda (a method used by
Donald G. Saari), and the example above, suggests that the Robla
listr owner is indeed able to moderate the EM List and get the
quality improved.

|>                              Very simple example:  4 candidates (A, B,
|>C, and D), 3 voters.  Here's the ballots:
|>
|>           Points for A    Points for B    Points for C    Points for D
|>A>B>C>D         4               3               2               1
|>A>B>C>D         4               3               2               1
|>B>C>D>A         1               4               3               2
|>
|>Totals:         9              10               7               4
|>
|>
|>B wins under Borda, even though B would lose in FPTP, IRV, Condorcet, and
|>most other methods.
...
|>Rob Lanphier

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```