# Reply to DEMOREP1's two examples

New Democracy donald at mich.com
Mon Feb 3 04:30:33 PST 1997

```DEMOREP wrote,
>A reminder- plain Approval Voting can directly violate head to head majority
>rule.
>
>Extreme example--
>51 AB
>49 B
>
>With AV, B gets 100, A gets 51, B wins.

Donald writes: Dear DEMOREP, Yes - but which one is correct?

Or - a better question would be: If Other Methods People are going to
consider other preferences as votes, are they going to consider them always
as votes - even when there is a majority in the first set of preferences?

Or - are the Other Methods people going to play bothe sides of the street.

I say that in your first example here the Apporval Voting method is
more honest than the Head to Head method. Approval Voting is considering
other preferences as votes under any conditions.

By the way: In this first example, Apporval Voting meets the Davison
Standard - Head to Head does not meet the Davison Standard. But - I must
also point out that this example is unrealistic - these results would never
occur in a real election in the real world - this example is proper here
because this list is not in the real world.

As examples become more real the Other Methods will all elect the same
candidate as elected by Preference Run-off.

DEMOREP wrote some more: >--------
>A slightly less extreme example--
>14 CE
>6   CD
>
>45 DC
>
>29 EC
>6   ED
>
>With AV, C gets 94, D gets 57, E gets 49, C wins.
>With head to head, D beats C, 51 to 49 and D beats E 51 to 49. D wins.

Donald writes: I will use your second example to show the math of the
Davison Standard. Each candidate will be tested using the following
equation:

Test of candidate A is equal to A(one) plus A(two) times --------------------

Test of candidate C = 20 + 74 X 45/(100-20) = 61.625

Test of candidate D = 45 + 12 X 45/(100-45) = 54.818

Test of candidate E = 35 + 14 X 45/(100-35) = 44.692

Candidate E received the lowest test amount and is dropped. The new vote
tally is as follows:

14 C
6 C    6 D
45 D   45 C
29 C
6 D
-----           We now have a candidate with a majority.
100             Candidate D is the winner with 51/100

Head to Head also elects the same candidate as Preference Run-off -
your second example is less exteme. I repeat: as examples become more real
the Other Methods examples will elect the Preference Run-off candidates.

Thank you DEMOREP for presenting these two examples - they allowed me to
show you some of my views - keep up the good work.

Yours Sincerely,

Donald Eric Davison of New Democracy at http://www.mich.com/~donald

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```