Brief Descriptions of Voting Methods, Errata-1

[Bruce Anderson]

Change:

Bucklin:
Let K(i) be the smallest value of k such that 
b(i,1)+...+b(i,k) > n/2.
Then I define Bucklin to select the candidate(s) that minimize K(i), with ties 
being broken by maximum b(i,1)+...+b(i,k), then by maximum b(i,1)+...+b(i,k-1), 
and so on.

to:

Bucklin and Bucklin-ext:  Let K(i) be the smallest value of k such that 
b(i,1)+...+b(i,k) > n/2.
Then Bucklin selects the candidate(s) that minimize K(i), with ties 
being broken by maximum b(i,1)+...+b(i,k), and Bucklin-ext continues to break 
ties (if needed) by maximum b(i,1)+...+b(i,k-1), then by maximum 
b(i,1)+...+b(i,k-2), ..., then by maximum b(i,1), then by maximum b(i,k+1), ..., 
and finally by maximum b(i,n).

Change:

Fishburn:  selects the candidate(s) that is (are) not a Fishburn losers.  A 
candidate, say i, is a Fishburn loser if there is some other candidate, say j, 
such that every candidate that pairwise beats j also pairwise beats i, and there 
is at least one candidate that pairwise beats i but does not pairwise beat j.

to:

Fishburn:  selects the candidate(s) that is (are) not a Fishburn loser.  A 
candidate, say i, is a Fishburn loser if there is some other candidate, say j, 
such that every candidate that pairwise beats j also pairwise beats i, and there 
is at least one candidate that pairwise beats i but does not pairwise beat j.

Change:

Schwartz:  selects the candidate(s) that is (are) not a Schwartz losers.  A 
candidate, say i, is a Schwartz loser if there are one or more other candidates, 
say j1,...,jm, such that j1 pairwise beats ... who pairwise beats jn who 
pairwise beats i, but there are not one or more other candidates, say k1,...,kn, 
where k1 is j1, such that i pairwise beats kn who pairwise beats ... who 
pairwise beats k1 who is j1.

to:

Schwartz:  selects the candidate(s) that is (are) not a Schwartz loser.  A 
candidate, say i, is a Schwartz loser if there are one or more other candidates, 
say j1,...,jm, such that j1 pairwise beats ... who pairwise beats jm who 
pairwise beats i, but there are not one or more other candidates, say k1,...,kh, 
where k1 is j1, such that i pairwise beats kh who pairwise beats ... who 
pairwise beats k1 who is j1.

Bruce