Instant-runoff voting: Difference between revisions

The "A Condorcet winner with over 1/3rd of 1st choice votes is guaranteed to win" [[Dominant mutual third|factoid]] can be used to speed up the counting; in the above example, when the votes were 8 B 9 D 5 C, D was a Condorcet winner:

{| class="wikitable"

|+Pairwise counting matrix

!

!A

!B

!C

!D

!E

|-

|A

| ---

|20 (+18 Win)

|15 (+8 Win)

|4 (-14 Loss)

|20 (+18 Win)

|-

|B

|2 (-18 Loss)

| ---

|8 (+6 Win)

|8 (+6 Win)

|11 (Tie)

|-

|C

|7 (-8 Loss)

|14 (-6 Loss)

| ---

|5 (-12 Loss)

|20 (+18 Win)

|-

|D

|18 (+14 Win)

|14 (-6 Loss)

|17 (+12 Win)

| ---

|20 (+18 Win)

|-

|E

|2 (-18 Loss)

|11 (Tie)

|2 (-18 Loss)

|2 (-18 Loss)

| ---

|}

When looking at only B, C, and D's matchups, this becomes:

{| class="wikitable"

|+Pairwise counting matrix

!

!B

!C

!D

|-

|B

| ---

|8 (-6 Loss)

|8 (-6 Loss)

|-

|C

|14 (+6 Win)

| ---

|5 (-12 Loss)

|-

|'''D'''

|'''14 (+6 Win)'''

|'''17 (+12 Win)'''

|'''---'''

|}

D [[Pairwise beat|pairwise wins]] against all others, and had 9 out of the 22 active votes = 40.9%, greater than 1/3rd, at that time. So there was no need to eliminate C at that point to find the winner.