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Modified Tennessee example with differing results

πŸ”— TNexampleSTARdiff     (tags: { theoretical })

Below is the ABIF from the "TNexampleSTARdiff" election (Modified Tennessee example with differing results)

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Voting methods: FPTP β€’ approval β€’ IRV β€’ STAR β€’ Pairwise β€’ All methods

Results

πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff

Below are the results of the election represented above using various election methods with abiftool/abiflib. The detected ballot type from the ABIF above is "rated". Some methods may transform these ballots for analysis; see method notices for details. Resubmit the ABIF with "Transform ballots" turned off to minimize the transformations.

Method Winner
FPTP Memphis, TN
Approval Nashville, TN
IRV/RCV Knoxville, TN
STAR Chattanooga, TN
Condorcet/Copeland Nashville, TN
Election results summary showing voting method winners
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FPTP result

"FPTP" is "First-past-the-post", also known as "plurality" or "choose-one"
TNexampleSTARdiff FPTP results permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/FPTP#FPTP
πŸ“
Note β€” FPTP run on ballot_type=rated

  • FPTP Winner: Memphis, TN with 42 first-place votes (42.0%)
  • Runner-up: Nashville, TN with 26 first-place votes (26.0%)
  • Margin of victory: 16 votes (16.0 percentage points)
  • First-place votes
    • Memphis, TN: 42 votes (42.0 %)
    • Nashville, TN: 26 votes (26.0 %)
    • Knoxville, TN: 17 votes (17.0 %)
    • Chattanooga, TN: 15 votes (15.0 %)
  • Total ballots: 100

Approval voting results

TNexampleSTARdiff approval voting results permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/approval#approval
πŸ“
Note β€” Approval counts estimated from 100 rated ballots using favorite_viable_half method
Details

The 'favorite_viable_half' conversion algorithm: find the candidate with the most first preferences, and then determine the minimum number of figurative seats that would need to be open in order for the candidate to exceed the Hare quota with the given first-prefs. We use this to estimate how many candidates are likely to be viable candidates.

Using first-choice vote totals as a rough guide, approximately 3 candidates appear viable: Memphis, TN, Nashville, TN, and Knoxville, TN. The approximation then assumes each voter approves up to 2 of their top-ranked viable candidates (half of 3, rounded up). All candidates ranked at or above the lowest-ranked of each ballot's top viable candidates receive approval (considering up to 2 viable candidates per ballot).

See transformed ballots

Note: For Approval, these choose_many ballots are inferred from rated ballots.

Conversion method: favorite_viable_half

#------- metadata -------
{ballotcount: 100}
{title: "Tennessee capitol example"}
{description: "This example ABIF file is contrived to cause a different score voting and STAR voting winner."}
{min_rating: "0"}
{max_rating: "5"}
#------ candlines ------
=Memph:[Memphis, TN]
=Nash:[Nashville, TN]
=Chat:[Chattanooga, TN]
=Knox:[Knoxville, TN]
#------- votelines ------
42:Memph/1=Nash/1
26:Chat/1=Knox/1=Nash/1
17:Chat/1=Knox/1=Nash/1
15:Chat/1=Knox/1=Nash/1
  • Approval Winner: Nashville, TN
  • Approval Results:
    • Nashville, TN (Nash) — 100 approvals (100.0% of ballots) (βœ… winner)
    • Chattanooga, TN (Chat) — 58 approvals (58.0% of ballots)
    • Knoxville, TN (Knox) — 58 approvals (58.0% of ballots)
    • Memphis, TN (Memph) — 42 approvals (42.0% of ballots)
  • Total: 100 ballots (258 total approvals)

IRV/RCV results

TNexampleSTARdiff IRV/RCV result permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/IRV#IRV

  • IRV/RCV Winner: Knoxville, TN with 58 votes (58.0%) in final round
  • Runner-up: Memphis, TN with 42 votes (42.0%) in final round
  • Exhausted ballots in final round: 0 (0.0%)
  • Number of rounds: 3
  • Ballots counted in final round: 100 (100.0%)
  • Majority of ballots: 51 (51.0%)
  • Total ballots: 100
Round 1 Round 2 Round 3
Overview:
Active ballots: 100 (100.0%)

Exhausted ballots: 0 (0.0%)
Counted ballots: 100 (100.0%)
Overview:
Active ballots: 100 (100.0%)

Exhausted ballots: 0 (0.0%)
Counted ballots: 100 (100.0%)
Overview:
Active ballots: 100 (100.0%)

Exhausted ballots: 0 (0.0%)
Counted ballots: 100 (100.0%)
Memphis, TN: 42 (42.0%)
β†’
Memphis, TN: 42 (42.0%)
β†’
Memphis, TN: 42 (42.0%) (πŸ›‘eliminated)
β†’
Nashville, TN: 26 (26.0%)
β†’
Nashville, TN: 26 (26.0%) (πŸ›‘eliminated)
β†’
Nashville, TN
Knoxville, TN: 17 (17.0%)
β†’
Knoxville, TN: 32 (32.0%)
β†’
IRV/RCV winner:
Knoxville, TN: 58 (58.0%)βœ…
β†’
Chattanooga, TN: 15 (15.0%) (πŸ›‘eliminated)
β†’
Chattanooga, TN Chattanooga, TN

STAR results

TNexampleSTARdiff STAR results permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/STAR#STAR

  • STAR winner: Chattanooga, TN
  • Finalists: Knoxville, TN vs Chattanooga, TN
  • Runoff result:
    • Knoxville, TN: 17 votes (17.0%)
    • Chattanooga, TN: 83 votes (83.0%)
    • No preference: 0 voters (0.0%)
  • Total stars allocated: 932
  • Total ballots: 100
β˜…β˜…β˜…β˜…β˜…β˜…

β˜…β˜…β˜…β˜…β˜…

β˜…β˜…β˜…β˜…β˜…β˜…
β˜…β˜…β˜…β˜…β˜…
β˜…β˜…β˜…β˜…β˜…β˜…
β˜…β˜…β˜…β˜…β˜…
β˜…β˜…β˜…β˜…β˜…β˜…
β˜…β˜…β˜…β˜…β˜…
β˜…β˜…β˜…β˜…β˜…β˜…
(one star above is approximately 19 stars allocated by voters)
  • First round:
    • β˜…#0: Knoxville, TN received 249 stars (26.7%) from 58 voters (58.0%)
    • β˜…#1: Chattanooga, TN received 247 stars (26.5%) from 58 voters (58.0%)
    • β˜…#2: Nashville, TN received 226 stars (24.2%) from 58 voters (58.0%)
    • β˜…#3: Memphis, TN received 210 stars (22.5%) from 42 voters (42.0%)
  • Finalists:
    • β˜…Knoxville, TN (βœ… winner) preferred by 17 of 100 voters
    • β˜…Chattanooga, TN preferred by 83 of 100 voters
    • β˜…No preference between the finalists: 0

Condorcet/Copeland results

TNexampleSTARdiff Condorcet/Copeland results permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/pairwise#pairwise
  • Winner: Nashville, TN
  • Runner-up: Chattanooga, TN (beats all other candidates except Nashville, TN)
  • Smallest margin: Nashville, TN over Memphis, TN (58-42; margin: 16)
  • Largest margin: Chattanooga, TN over Knoxville, TN (83-17; margin: 66)
  • Pairwise ties: none
  • Total ballots: 100

Win-loss-tie (Condorcet/Copeland) table

TNexampleSTARdiff w-l-t table permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/pairwise#wlt
Modified Tennessee example with differing results pairwise matchups
Nashville, TN
(3-0-0)
Nashville, TN
3 victories ⇣
Chattanooga, TN
(2-1-0)
Nashville, TN: 68(68.0%)
Chattanooga, TN: 32(32.0%)
(No preference: 0; 0.0%)
Chattanooga, TN
⇽ 1 loss / 2 victories† ⇣
Knoxville, TN
(1-2-0)
Nashville, TN: 68(68.0%)
Knoxville, TN: 32(32.0%)
(No preference: 0; 0.0%)
Chattanooga, TN: 83(83.0%)
Knoxville, TN: 17(17.0%)
(No preference: 0; 0.0%)
Knoxville, TN
⇽ 2 losses / 1 victory† ⇣
Memphis, TN
(0-3-0)
Nashville, TN: 58(58.0%)
Memphis, TN: 42(42.0%)
(No preference: 0; 0.0%)
Chattanooga, TN: 58(58.0%)
Memphis, TN: 42(42.0%)
(No preference: 0; 0.0%)
Knoxville, TN: 58(58.0%)
Memphis, TN: 42(42.0%)
(No preference: 0; 0.0%)

Pairwise tournament (Copeland ordered)

TNexampleSTARdiff pairwise diagram permalink:
πŸ”—https://abif.electorama.com/id/TNexampleSTARdiff/pairwise#dot

%3 Nash Nash 3-0-0 (3 wins, 0 losses, 0 ties) Chat Chat 2-1-0 Nash->Chat ← Nash: 68 Chat: 32 Knox Knox 1-2-0 Nash->Knox ← Nash: 68 Knox: 32 Memph Memph 0-3-0 Nash->Memph ← Nash: 58 Memph: 42 Chat->Knox ← Chat: 83 Knox: 17 Chat->Memph ← Chat: 58 Memph: 42 Knox->Memph ← Knox: 58 Memph: 42

Voting methods: FPTP β€’ approval β€’ IRV β€’ STAR β€’ Pairwise β€’ All methods

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