Fractional vs Random Selection

[New Democracy]

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Dear List members,

     Someday you may face the decision of whether to use fractional or
random selection when votes are to be transferred in the working of
Preference Voting. In all fairness to bothe the candidates and the voters
that elect these candidates you should use the method of transfer that is
most accurate.

     In a Preference Voting election if we were to work the ballots a
second time would we get the same results? If we were using fractional
transfer of the votes we would get the same results because the math would
be the same each and every time - this will not be true with random
transfer.

     When I made my study of a vacancy on the council I used fractional
transfer in the Preference Voting method. I noticed that I had two
candidates in two separate rounds that were dropped because they were only
one half of a vote in last place. A third candidate was last by only one
vote on another round. It is not the fault of fractional transfer that
these number are so close - on the contrary it is to the credit of
fractional transfer that it is able to detect this small difference.

     This closeness made me think that randon selection transfer would have
results that would be off this mark set by fractional transfer. I reasoned
that the fractional splitting of the votes is able to make an accurate
division between who gets dropped and who is allowed to stay in for the
current round.

     I proceeded to make another study of a vacancy on the council but this
time I used random selection transfer. This resulted in a different
candidate winning the last spot on the council. The last candidate to be
dropped was only one vote behind.

     I made a third study of a vacancy on the council and again I used
random selection transfer of votes - but the random votes used this time
were different from the random votes used in study election number two. The
results of this third time had the same candidates elected as number two -
but the last candidate to be dropped was now three votes behind.

     These last two studies using different random selections for
transferring votes, produced the same winners but I feel that at another
time in another election it is posssible to get different sets of winning
candidates. Random transfer causes vote counts to be two or three or more
votes one way or another per candidate. It is important to use the
fractional transfer of excess votes instead of random selection.

     Fractional division can also be used when we manual sort ballots. All
the ballots of a candidate with an excess are to be stamped with the amount
of the part of the vote that is to be transferred - then all the ballots
are transferred by hand to the pile of the candidate that is the next
preference.

     For example: Suppose a candidate had twenty-five percent more votes
than a share - that candidate is elected and the number .2000 would be
marked on all ballots of this candidate. This means that now all these
ballots are only worth one fifth of a vote. All these ballots would be
transferred to the pile of the next preference on each ballot. Now whenever
a pile is counted any ballot marked with .2000 is to be only counted as
.2000 of a vote.

     There is another time in which fractional division is to be used
besides the transfer of excess votes. When votes are transferred to a
candidate that is near the share the transfer may put this candidate over
the share amount needed. In these cases all the votes being transferred on
this round to this one candidate are to be divided using fractional
division - leaving the candidate with the correct size part per ballot that
will give him enough votes to match the share amount. The other parts of
these ballots go to the next preferences on the ballots. This can happen
either when excess votes are being transferred or when votes of dropped
candidates are being transferred.

     Some of the ballots may already be marked with a fraction - if so
those ballots get marked with a value that is the old fraction times the
current fraction being used on the current votes being transferred to a
candidate.
Example: .2000 X .5420 = .1084 is the new value to be marked on these ballots.

This is letter Five in a series dealing with the Cambridge Ballots.

Yours,

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

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