# [EM] Single Winner math basics

Steve Eppley seppley at alumni.caltech.edu
Mon Mar 4 23:34:16 PST 1996

```DEMOREP1 at aol.com wrote:
>It becomes necessary again to state single winner math basics.
>A voter has a range of 100 percent approval to minus 100 percent
>disapproval

Demorep1, your writing these last few weeks has become much easier
to understand.  But there are still some significant differences in
terminology that we have to watch out for.  If your method above is
what you've meant by Approval in recent messages, be advised that
most electoral reformers mean something very different!  The more
common meaning is that each voter gets only a binary choice on each
candidate (yes or no, approve or disapprove, whatever), not such a
finely graded ballot as -100 to +100.

Before Rob launched the election-methods list, several of us
conducted a few weeks of discussion about single-winner methods using
ordinary group cc:s.  I inquired about a voting method I called
"rated ballots", the same in essence as your -100 to +100 though the
scale might vary (0 to 10, -10 to 10, 0 to 100, etc.)

Mike Ossipoff pointed out to me that though the Rated ballot can
offer the voters more expression than the Ranked ballot, in practice
voters will often vote tactically instead of honestly: they'll tend
to rate only using only the two endpoints of the range. Empirically,
use of these tactics is widespread enough that they essentially turn
it into the binary Approval ballot, which provides less voter
expression than Ranked ballots.

One other thing which makes it hard to understand some of your
writing is that you don't quote any text from the message(s) to which
you're replying.  It can be a chore to determine the context without
inclusion of key paragraphs.  Does your email software make it hard
for you to copy the original into your reply?  Most email software
does this automatically, and also automatically prefixes each line
with a '>' character to make the nested quotes readily apparent.

>The potential of plain Condorcet for electing candidates with
>disapproval votes (first choice or a later choice) is absolutely
>critical.

I don't know if you've had time to read all the other posts in this
list, but many of them have been about a "nonplain" Condorcet which
will deny election to majority-disapproved candidates.  Look for
messages about Condorcet+NOTB (None of the Below).

As to whether it's critical to have this safeguard, for me it's a
tough call.  It ought to be a rarity when this happens, so is the
added complexity of the method justified?  Will the extra "wrinkle"
make it harder to persuade the electorate to switch to it from the
existing system?

>How many EM folks want zero to minus 100 percent disapproval votes
>to be used to help elect anybody ?

Not me!

>Thus, there is the multiple same choices (MSC) remedy. Each voter
>may approve one or more candidates for the office using multiple
>same choices (a voter votes 0, 1, 2, 3, etc. for each candidate or
>leaves a blank by the candidate).

Here we've got another terminology problem.  It looks like you're
describing a voting method we've never clearly defined, so there may
be some confusion for awhile.

Some recent messages have discussed the variation of Condorcet which
allows multiple candidates to be ranked equally.  If you review,
you'll find several messages entitled "Re: Multiple Same Choices"
is when MSC entered our lexicon, but your description of MSC then
was incomplete and hard for me to understand.

>A 0 or blank vote would be a disapproval vote. NOTA would be
>shorthand for a 0 vote for all candidates.

This is a 0 to 100 ballot?

To use the NOTA shorthand, the voter must be able to sort the
candidate list?

>Step. 1. Candidates with majority 0 votes plus blanks would lose.
>
>Step. 2. If 2 or more other candidates remain, then Condorcet may
>be used as a tie-breaker (assuming computer voting is available with
>a large number of voters).

Is this "Condorcet" different from conventional Condorcet?  This one
uses the ratings in its pairwise comparisons, right?

Example:
one ballot:      A=99   B=50
another ballot:  A=60   B=61

Does MSC's Condorcet score A vs B at (49-1) or tied?

>Question- Should a Condorcet winner (winning all pair matches or in
>a tie breaker) be allowed to be elected with a plurality only
>(highly possible with truncated voting) ?

What is the meaning of plurality in a rated ballot?

>Step 3. If no candidate gets elected, then have a new election or
>have the majority rule P.R. legislative body appoint the officer.

There have been some other proposals for dealing with this too, like
a shortened term of office for the least-disapproved, or letting the
least-disapproved serve until the new election succeeds in electing
someone.

--Steve

```