[EM] Symmetrical ICT program with missing line included

[Michael Ossipoff]

Where I'd said "(If some but not all candidates are unbeaten:)", I'd
neglected to add, below that, the program statement that contains that
"if":

If NBeaten > 0 AND NBeaten < NC

Also, instead of just specifying that the section is the same as the
previous one except for two changes, I should write the section out.

So the program-listing below is complete. As before, it is preceded by
some explanatory text, since this posting is intended to replace the
previous one.

This pseudocode is for counting Symmetrical ICT, a rank-count which, I
claim, avoids the strategy problems otherwise distort voters sincere
expression of preferences--does so better than any other rank-count.

It meets FBC; is defection-resistant (maning that it avoids the
Chicken Dilemma); meets the Condorcet Criterion, if equal-top-ranking
and equal-bottom-ranking are counted consistent with the intent and
wishes of people voting in that way; and meets LNHe.

The program will be divided into numbered and named sections. There
may be comments here and there. If so, they'll be in parentheses,
sometimes on their own line (in which case they refer to what's below
them if they end in a colon--otherwise they refer to what's above
them). Maybe sometimes they'll be at the end of a line, referring to
that line.

The Symmetrical ICT count pseudocode:

(I have an initialization section that initializes a number of global
variables. I usually also initialize them at the appropriate place in
the program too. No harm in doing it twice.)

NC is the number of candidates. NB is the number of ballots.

R(k,i) is the array for the rank at which candidate i is ranked on ballot k.

1. Initialization:

NBeaten = 0 (No one initially beaten)

(Initialize everyone unbeaten:)
For i = 1 to NC
...Beaten(i) = 0
...Win(i) = 0
...NTop(i) = 0
Next i

(Initialize everyone at bottom on every ballot:)
For k = 1 to NB
...For i = 1 to NC
......Bottom(k,i) = 1
...Next i
Next k

(Initialize all the pairwise totals to zero:)
For i = 1 to NC
...For j = 1 to NC
...V(i,j) = 0  (votes for i over j)
...ET(i,j) = 0 (ballots with i and j top ranked)
...EB(i,j) = 0 (ballots with i and j at bottom)
Next j
Next i

(at bottom means not ranked over anyone on that ballot)

(Below, some of the indentation isn't correct, because it was
necessary to fix an error)

2. Pairwise totals:

(i's top-count, i-j pairwise vote totals and equal-top:)

For k = 1 to NB
...For i = 1 to NC
......If R(k,i) = 1 then:
......Top(k,i) = 1
.......NTop(i) = NTop(i) + 1
......Endif
......For j = 1 to NC
.........If R(k,i) < R(k,j) then
............V(i,j) = V(i,j) + 1
.........Endif
.........If R(k,i) = 1 AND R(k,j) = 1 AND i<>j then
............ET(i,j) = ET(i,j) + 1
.........Endif
......Next j
...Next i

(Is i at bottom on ballot k?:)

For i = 1 to NC
...For j = 1 to NC
......If  R(k,i) < R(k,j) then
.........Bottom(k,i) = 0 (i is not at bottom)
......Endif
...Next j
Next i

(Increment i-j equal bottom count?:)

For i = 1 to NC
...For j = 1 to NC
......If Bottom(k,i) = 1 AND Bottom(k,j) = 1 AND i<>j then
.........EB(i,j) = EB(i,j) +1
......Endif
...Next j
Next i
Next k

3. Is candidate i unbeaten?

For i = 1 to NC
...For j = 1 to NC
......If V(j,i) + EB(i,j) > V(i,j) + ET(i,j) then
.........Beaten(i) = 1
......Endif
...Next j
...If Beaten(i) = 1 then
......NBeaten = NBeaten + 1
...Endif
Next i

4. Find winners:

(If exactly 1 candidate is unbeaten:)

If Nbeaten = NC - 1 then:
...For i = 1 to NC
......If Beaten(i) = 0 then
.........Win(i) = 1
.........Print Name(i), "_Wins."
......Endif
...Next i
Stop
Endif

(If all or no candidates are unbeaten:)

(Find maximum top-score:)
If NBeaten = 0 OR NBeaten = NC
...Max = 0
...For i = 1 to NC
......If NTop(i) > Max then:
.........Max = NTop(i)
......Endif
...Next i


(Find who has that top-score:)

...For i = 1 to NC
......If NTop(i) = Max then:
.........Win(i) = 1
.........Print Name(i), "_Wins."
......Endif
...Next i
Stop
Endif

(If some but not all candidates are unbeaten:)

If NBeaten > 0 AND NBeaten < NC

(Find maximum top-score:)

...Max = 0
...For i = 1 to NC
......If NTop(i) > Max AND Beaten(i) = 0 then:
.........Max = NTop(i)
......Endif
...Next i


(Find who has that top-score:)

...For i = 1 to NC
......If NTop(i) = Max AND Beaten(i) = 0 then:
.........Win(i) = 1
.........Print Name(i), "_Wins."
......Endif
...Next i
Stop
Endif

[End of program]

Here is rudimentary code to manually enter rankings into the program:

For k = 1 to NB
...For i = 1 to NC
......Print Name(i)
......Input "Rank", R(k,i)
...Next i
Next k

[end of manual ranking-entry program]

As I said, if that manual ranking-entry program is used, then it
should be appended to the beginning of the main program described
above.