# [EM] (Fwd) STV and truncation

Mike Ossipoff dfb at bbs.cruzio.com
Thu Apr 4 21:32:55 PST 1996

```Excuse my late reply--I've been very wrapped up in single-winner
debates.

Probably most fractional STV wordings simply leave "exhausted"
(removed from the election) any vote value of a nontransferable
ballot.

But there's a fairly popular version that doesn't do that:

When a candidate is elected with surplus, we could calculate
his "transfer fraction" differently.

The usual transfer fraction, in U.S. fractional STV proposals,
is s/v, where s = the candidate's surplus, and v = his vote total.
Then, or course, each of his transferable ballots has its value
multiplied by this "transfer fraction" before it's transferred.

But there's a better way to do it:

Where s = the candidate's surplus
&     t = the combined vote value of his transferable ballots
&     F = his transfer fraction

F = min (s/t, 1)

..which means s/t or 1, whichever is less.

***

This rule automatically transfers as much of the candidate's
surplus as possible. And it automatically lets each voter transfer
all of his extra vote value.

If you don't list a next choice, surely you don't mind if the
other ballots transfer as much of _their_ incoming vote value
as possible, without transferring more than the candidate's
surplus.

I emphasize that, since F can't be more than 1, no ballot is
transferring value that is anyone else's. If you don't list
a next choice, that _doesn't_ mean that someone else is allowed
to transfer your vote value with their ballot. All it means is
that the transferable ballots should be allowed to tranfer
as much of their value as possible, as long as they don't
transfer more than the value that they arrived with, and as
long as they don't transfer more then the candidate's surplus.

F = min (s/t, 1) carries this out.

That's the surplus transfer fraction that we used in our
Santa Cruz initiative. We weren't the 1st to use or propose
it, however.

***

Now, that's basic, but, if complication weren't an object, why
not give the voter the option to indicate that if there should
come a time in the count when his allot lists nowhere for it to
go, that voter would like to re-assign his vote value to the
other ballots of that candidate? After all, if those other voters
have their ballots on the same candidate that you do, then
wouldn't they be more likely to be people whose judgement you
could trust for subsequent choices?

It turns out that this can be accomplished  by merely changing
the candidate's transfer fraction, based on the number of voters
who want to send their vote value witht he other ballots of
that candidate.

***

Another possibility, which would require more computation, and would
be quite out of the question in a hand-count (as fractional STV
pretty much already is) would be to give voters the option to
assign the vote value of their exhausted ballots to the other
ballots in the election which are still tranferable and which
share the same 1st choice. So if your ballot has nowhere to go,
and you've punched the box to incicate that you're using that
option, then your ballot's value is divided among the other

***

It's important to emphasize that these "optional re-assignment"
possibities should only be options, and shouldn't be done automatically
without the voter's consent.

***

As I said, the 1st one, which gives a voter the option to indicate
that, should his ballot have nowhere to go, he'd like to
send its vote value along with the transferable ballots of the
candidate from whom that voter doesn't list a next choice--this
option is very easily & simply implemented, just by calculating
the transfer fraction by a different formula, which takes into
account the combined vote value of the exhausted ballots using
that option.

***

I feel that 1 of these 2 "optional reassignment" options would
be a good thing in STV. We didn't use them in Santa Cruz, for
simplicity's sake. They'd mean that a voter could vote a short
ranking, if he/she doesn't know about many candidates, while
still being sure of taking part in a possible majority coalition
with voters with whom he/she agrees.

But, just as we didn't include either in our Santa Cruz proposal,
I wouldn't recommend the added complication of such rules in
an initial STV proposal.

***

Mike Ossipoff

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