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Pandora's Tale Wiki:Pandora's Tale Volume 1 Character Tournament: Difference between revisions
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===Tiebreakers===
A tie only matters if there is a tie for <math>\lceil\frac{\text{Number of characters in the match}}{2}\rceil</math>'th place. When such a tie occurs, the following rules were used for tiebreakers:
#If all characters in a match are tied, then the tournament organizer's votes (i.e. my votes) are discarded.
#Otherwise, if more than half of the characters are tied for last place, then all of the characters tied for last place are eliminated.
#Otherwise, the tie will be resolved by allowing more characters to advance to the next round.
Rule (2) ensures that at least once character is eliminated in every match. It was intended to prevent the possibility of an infinite loop. Rules (1) and (3) were intended to reduce the likelihood that a popular character would be eliminated early just because of random match-ups.
===Semifinal Placement===
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When five or fewer characters remain at the end of a round, the following round constitutes the start of the semifinals. Characters are placed into the semifinals based on their vote-shares in previous rounds. A character's ''vote-share'' for a match is defined to be the number of votes they got divided by the total number of votes in the match. Their ''average vote-share'' is the arithmetic mean of their vote-shares in matches prior to the semifinal. All matches are weighted equally, not by the number of votes.
All semifinal and final matches are one-vs-one. Hence, the only tie-breaker rule that could come into effect is the rule that when the entire match is tied, the tournament organizer's vote is discarded.
Unlike all matches prior to the semifinals, each semifinal and final match lasts two weeks, except for the "third-place match" if applicable.
How exactly the semifinalists are placed depends on the number of semifinalists. Note that without tiebreakers, there will always be exactly four semifinalists.
====5 Semifinalists====
The semifinalists with the 4<sup>th</sup> and 5<sup>th</sup> highest average vote-shares face off against each other in a "pre-semifinal" match. The loser is awarded 5<sup>th</sup> place and eliminated from the tournament. The tournament then proceeds as if there were only four semifinalists.
====4 Semifinalists====
The semifinalists with the highest and 4<sup>th</sup> average vote-shares face each other in one match, and the characters with the 2<sup>nd</sup> and 3<sup>rd</sup> highest average vote-shares face each other in another semifinal match.
The losers of the two semifinals then face each other in a "third-place match." Unlike all other semifinals, the third place match lasts only one week. The loser is awarded 4<sup>th</sup> place while the winner is awarded 3<sup>rd</sup> place.
Finally, the winners of the semifinals face each other in a 2-week final match.
====3 Semifinalists====
The semifinalists with the 2<sup>nd</sup> and 3<sup>rd</sup> highest average vote-shares face each other in a semifinal match. The loser is awarded third place and eliminated, while the winner faces the character with the highest average vote-share in the final.
====2 Semifinalists====
The semifinals are unnecessary, and the only two "semifinalists" immediately face each other in the final match.
===Motivation for the Rules===
The intent of these rules was to meet two simultaneous goals:
# There should be a high probability that the strongest two candidates make it to the finals. A single-elimination tournament with 1-vs-1 matches was therefore undesirable, since the two most popular characters could be randomly paired against each other in the first round. The system I wrote allows multiple characters to advance in each match prior to the semifinals, and the fact that each voter can vote for multiple candidates reduces the likelihood that the front-runner will be eliminated due to vote-splitting.
# The tournament should happen in a reasonable time frame even for a large initial cast. A double-elimination tournament of 1-vs-1 matches would require 38 matches, and even a single-elimination tournament would require 19. This system allowed the tournament to conclude with match 13.
==Detailed Results==
===Part 1===
The first match consisted of four matches, each with five characters.
====Match 1====
* Veronica Fortuna: 8 (including the tournament organizer)
* Gabriel Glenholm: 0 (Eliminated)
* Maple: 5
* Lyra Lujic: 2 (Eliminated)
* Con Yung: 4
====Match 2====
* Hemmel: 3 (including the tournament organizer)
* Natalya Ustrashkina: 4 (including the tournament organizer)
* Tallulah Zaragoza: 3
* Petrichor: 1 (eliminated)
* Cassiopeia: 0 (eliminated)
====Match 3====
* Andromeda: 6
* Isabelle Monday: 9 (including the tournament organizer)
* Noor Shah: 10 (including the tournament organizer)
* Eric Fishguard: 0 (eliminated)
* Zero Angiers: 2 (eliminated)
====Match 4====
* Hamilton Smith-Rawnsley: 0 (eliminated)
* Pandora: 12 (including the tournament organizer)
* Adrastea: 5
* Leo: 4
* Zufolene: 4 (including the tournament organizer)
Four characters received zero votes. Three of those characters are villains with no redeeming qualities (Gabriel Glenholm, Eric Fishguard, and Hamilton Smith-Rawnsley). Cassiopeia is the only non-villain to receive no votes
===Part 2===
====Match 5====
* Hemmel: 6 (including the tournament organizer)
* Natalya Ustrashkina: 7 (including the tournament organizer)
* Veronica Fortuna: 8 (including the tournament organizer)
* Adrastea: 4 (eliminated)
* Zufolene: 1 (eliminated)
====Match 6====
* Tallulah Zaragoza: 0 (eliminated)
* Isabelle Monday: 5 (including the tournament organizer)
* Maple: 1 (eliminated)
* Pandora: 6 (including the tournament organizer)
====Match 7====
* Noor Shah: 9 (including the tournament organizer)
* Con Yung: 4 (including the tournament organizer)
* Leo: 0 (eliminated)
* Andromeda: 4
===Part 3===
====Match 8====
* Isabelle Monday: 4 (including the tournament organizer)
* Andromeda: 2 (eliminated)
* Noor Shah: 3
* Pandora: 3 (including the tournament organizer)
====Match 9====
* Hemmel: 4
* Natalya Ustrashkina: 7 (including the tournament organizer)
* Con Yung: 4
* Veronica Fortuna: 2 (including the tournament organizer) (eliminated)
Along with the announcement of Match 9, Xan said "We've officially reached the "All main characters apart from Zero" point of the poll." <ref>https://nitter.unixfox.eu/ComicsByXan/status/1485749026871918594#m</ref>{{ArchiveNeeded}}
===Part 4===
====Match 10====
* Natalya Ustrashkina: 5 (including the tournament organizer)
* Hemmel: 3 (including the tournament organizer)
* Con Yung: 2 (eliminated)
====Match 11====
* Pandora: 4 (including the tournament organizer) (eliminated)
* Isabelle Monday: 4 (including the tournament organizer) (eliminated)
* Noor Shah: 5
Arguably the highlight of the tournament, Match 11 saw Noor trigger the tiebreaking rules to eliminated both of the main characters, clearing the stage for the semifinal.
===Part 5===
With only three characters remaining, characters were placed into the semifinal based on their vote shares in prior rounds. The "vote share" of a character in a given match is defined to be the number of votes the character got divided by the total number of votes in the match. Semifinalists were placed based on the arithmetic mean of the vote shares the received in rounds 1-4.
{| class="wikitable"
|+ Average vote shares
|-
! Character !! Average vote share
|-
| Natalya || 3755/9724≈0.38616
|-
| Doctor Shah || 36623/95472≈0.38360
|-
| Hemmel || 25253/97240≈0.25970
|}
Natalya had the highest vote share, so she was automatically placed in the final.
====Match 12====
* Hemmel: 3 (including the tournament organizer) (eliminated)
* Noor Shah: 11
Doctor Shah easily won the semifinal.
===Part 6===
===Match 13===
* Natalya Ustrashkina: 5 (including the tournament organizer) (eliminated)
* Noor Shah: 11 (winner)
Doctor Shah won the tournament.
==Aftermath==
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