# [EM] Single Winner math basics

DEMOREP1 at aol.com DEMOREP1 at aol.com
Mon Mar 4 21:33:48 PST 1996

```It becomes necessary again to state single winner math basics.

A voter has a range of 100 percent approval to minus 100 percent disapproval
for each candidate in a single winner election ( a 200 percent range) (with
an additional possible unknown/ don't care vote for those candidates whom the
voter does not take the time or effort to learn about).

Thus, in an election with three candidates (X, Y and Z)--

Voter A could vote-
X 100
Y   99
Z   98

Voter B could vote-
X  -98
Y  -99
Z  -100

With plain Condorcet each voter would be voting relatively the same.

If above zero values are deemed approval and below zero (minus) values are
deemed disapproval in Approval Voting, then Voter A approves all three
candidates and Voter B disapproves all three candidates.

Unfortunately, as mentioned sometime ago, percentage values cannot be used
since there is one whole candidate being elected and not some positive or
negative percentage of him/her (accumulated somehow from all voters).

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

The extreme case would be if a majority of the voters each voted minus 98 as
their first choice for candidate X (or using second choices X wins all
candidate pairs using minus 98, minus 99 and/or minus 100 votes if all voters
ranked all candidates in some combination of minus 98, minus 99 and minus
100). With plain Condorcet, candidate X would be elected.

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

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).

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

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).

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) ?

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

Attention Condorcet fans- Step 1 is a safety valve addition to pure/plain
Condorcet.
Step 2 means voting 1, 2, etc. would be a vote in the 100 percent to 0
percent approval range.

For computer programmer folks- a 1, 2, etc. vote would each beat 0 or blank
in Condorcet pair comparisons. If a voter votes in MSC for two or more
candidates at the same level (such as voting 1 for two or more candidates),
then each candidate gets 1 vote in Condorcet pair comparisons (not zero or
0.5 vote).

Thus in the recent Hitler-Stalin-Middle examples, Step 1 would be computed
first (with possibly each candidate having a majority disapproval).

Note- The above technically also applies with any single transferrable vote
proportional representation system for legislative bodies. However, since it
is possible for each voter to elect a legislative body member in multi-member
districts or at large, the minus percentages of plain Condorcet are greatly
reduced and the 0 or blank make no sense (unless a majority 0/blank vote for
all candidates means that the legislative body is not elected).

```