Bare majority winners

[DEMOREP1 at aol.com]

Variations of the bare majority winner idea for single winners can be used in
multiple executive/ judicial elections and proportional representation
elections.

Elect 2 or more executive/ judicial officers

Example- Elect 3 sheriffs (i.e. top 3 choices of each voter count)

5 of 7 candidates in a circular tie, each gets a YES majority acceptability
vote.  
Using the number votes, the combination in which 1 of the 5 gets the most
votes but loses would be the tiebreaker.
That is--
W= winner, HL = highest loser, OL = Other losers
    W1  W2   W3   HL  OL1   OL2   OL3   First Choice votes
+   N1   N2    N3   NHL                          + 2nd plus choice votes
    T1   T2    T3   THL                           Total votes

T1 or T2 or T3 > THL
The final result would have the THL votes being counted for W1, W2 or W3 using
the next choices.

Proportional representation elections

Elect 5 in a district, 10 candidates, 1 vote from each voter is to be
effective, only number voting is used.
Assume 2 candidates win in all of their combinations using number voting and 3
candidates lose in all of their combinations (i.e. 5 candidates are in tie for
3 positions).

This might happen if a party has major splits among its candidates.

The math is the same as above but only 1 choice is effective.

THL is the highest but T1 or T2 or T3 or T4 or T5 > THL  

This means that all or some of the first choice minorities (5) could not unite
behind 1 candidate to displace 1 of the winners.

The final result would have the THL votes being counted for W1, W2, W3, W4 or
W5 using the next choices.
Each winner would have a voting power equal to the final votes received.