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A modified version of the Tennessee example which demonstrates an IRV tie

🔗 TNexampleTie     (tags: { theoretical , CondorcetVsIRV , featured , IRVtie })

Below is the ABIF from the "TNexampleTie" election (A modified version of the Tennessee example which demonstrates an IRV tie)

ABIF submission area (show)
Method options
Ballot options

Voting methods: FPTP • approval • IRV • STAR • Pairwise • All methods

Results

🔗https://abif.electorama.com/id/TNexampleTie

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, Memphis, TN
STAR Memphis, TN, Knoxville, TN
Condorcet/Copeland Nashville, TN, Memphis, 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"
TNexampleTie FPTP results permalink:
🔗https://abif.electorama.com/id/TNexampleTie/FPTP#FPTP
📝
Note — FPTP run on ballot_type=rated

  • FPTP Winner: Memphis, TN with 42 first-place votes (50.0%)
  • Runner-up: Nashville, TN with 20 first-place votes (23.8%)
  • Margin of victory: 22 votes (26.2 percentage points)
  • First-place votes
    • Memphis, TN: 42 votes (50.0 %)
    • Nashville, TN: 20 votes (23.8 %)
    • Knoxville, TN: 12 votes (14.3 %)
    • Chattanooga, TN: 10 votes (11.9 %)
  • Total ballots: 84

Approval voting results

TNexampleTie approval voting results permalink:
🔗https://abif.electorama.com/id/TNexampleTie/approval#approval
📝
Note — Approval counts estimated from 84 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: 84}
{title: "Tennessee capitol example"}
{description: "Hypothetical example of selecting capitol of Tennessee, only this time representing a tie election rather than an outright win."}
#------ candlines ------
=Memph:[Memphis, TN]
=Nash:[Nashville, TN]
=Chat:[Chattanooga, TN]
=Knox:[Knoxville, TN]
#------- votelines ------
42:Memph/1=Nash/1
20:Chat/1=Knox/1=Nash/1
12:Chat/1=Knox/1=Nash/1
10:Chat/1=Knox/1=Nash/1
  • Approval Winner: Nashville, TN
  • Approval Results:
    • Nashville, TN (Nash) — 84 approvals (100.0% of ballots) (✅ winner)
    • Memphis, TN (Memph) — 42 approvals (50.0% of ballots)
    • Chattanooga, TN (Chat) — 42 approvals (50.0% of ballots)
    • Knoxville, TN (Knox) — 42 approvals (50.0% of ballots)
  • Total: 84 ballots (210 total approvals)

IRV/RCV results

TNexampleTie IRV/RCV result permalink:
🔗https://abif.electorama.com/id/TNexampleTie/IRV#IRV
⚠️
Note — Round 3 tiebreaker used
Details

In Round 3, Knoxville, TN and Memphis, TN were tied with exactly 42 votes each in the final round. Since this is a tie for the most votes in the final round, both candidates are declared IRV winners. In a real election, this might be resolved by lot drawing or other official tiebreaker procedure depending on jurisdiction.

  • IRV/RCV Winners (tie): Knoxville, TN, Memphis, TN with 42 votes (50.0%) in final round
  • Runner-up: Memphis, TN with 42 votes (50.0%) in final round
  • Exhausted ballots in final round: 0 (0.0%)
  • Number of rounds: 3
  • Ballots counted in final round: 84 (100.0%)
  • Majority of ballots: 43 (51.2%)
  • Total ballots: 84
Round 1 Round 2 Round 3
Overview:
Active ballots: 84 (100.0%)

Exhausted ballots: 0 (0.0%)
Counted ballots: 84 (100.0%)
Overview:
Active ballots: 84 (100.0%)

Exhausted ballots: 0 (0.0%)
Counted ballots: 84 (100.0%)
Overview:
Active ballots: 84 (100.0%)

Exhausted ballots: 0 (0.0%)
Counted ballots: 84 (100.0%)
TIE(†): Knox, Memph
Memphis, TN: 42 (50.0%)
→
 Memphis, TN: 42 (50.0%)
→
 IRV/RCV winner:
Memphis, TN: 42 (50.0%)✅
→
Nashville, TN: 20 (23.8%)
→
 Nashville, TN: 20 (23.8%) (🛑eliminated)
→
 Nashville, TN
Knoxville, TN: 12 (14.3%)
→
 Knoxville, TN: 22 (26.2%)
→
 IRV/RCV winner:
Knoxville, TN: 42 (50.0%)✅
→
Chattanooga, TN: 10 (11.9%) (🛑eliminated)
→
 Chattanooga, TN Chattanooga, TN
† - This example employs a limited form "batch elimination", where a batch of multiple candidates who (in sum total) do not have enough remaining top preferences to defeat the next highest candidate in the rankings. †† - When a tie occurs, per the laws in the City and County of San Francisco and the laws in the state of Maine, the losing candidate for the round is randomly eliminated.

STAR results

TNexampleTie STAR results permalink:
🔗https://abif.electorama.com/id/TNexampleTie/STAR#STAR
⚠️
Note — STAR runoff ended in tie
Details

In the STAR runoff, Memphis, TN and Knoxville, TN were tied with exactly 42 votes each out of 84 total voters. This represents a perfect tie in the automatic runoff between the top two scoring candidates. In a real election, this might be resolved by lot drawing or other official tiebreaker procedure depending on jurisdiction.

  • STAR winner: Knoxville, TN, Memphis, TN
  • Finalists: Knoxville, TN vs Memphis, TN
  • Runoff result:
    • Knoxville, TN: 42 votes (50.0%)
    • Memphis, TN: 42 votes (50.0%)
    • No preference: 0 voters (0.0%)
  • Total stars allocated: 23,926
  • Total ballots: 84
★★★★★★

★★★★★

★★★★★★
★★★★★
★★★★★★
★★★★★
★★★★★★
★★★★★
★★★★★★
(one star above is approximately 479 stars allocated by voters)
  • First round:
    • ★#0: Knoxville, TN received 6,690 stars (28.0%) from 62 voters (73.8%)
    • ★#1: Memphis, TN received 5,870 stars (24.5%) from 42 voters (50.0%)
    • ★#2: Nashville, TN received 5,780 stars (24.2%) from 22 voters (26.2%)
    • ★#3: Chattanooga, TN received 5,586 stars (23.3%) from 42 voters (50.0%)
  • Finalists:
    • ★Knoxville, TN (✅ winner) preferred by 42 of 84 voters
    • ★Memphis, TN preferred by 42 of 84 voters
    • ★No preference between the finalists: 0

Condorcet/Copeland results

TNexampleTie Condorcet/Copeland results permalink:
🔗https://abif.electorama.com/id/TNexampleTie/pairwise#pairwise
📝
Note — Condorcet cycle or Copeland tie
Details

This election has no Condorcet winner. Nashville, TN and Memphis, TN are tied for the most pairwise victories (Copeland tie). Each of these candidates beats the same number of opponents in head-to-head comparisons, creating a cycle in the tournament. The Copeland/pairwise table below shows the detailed win-loss-tie records that result in this tie.

  • No Condorcet winner: Copeland tie betweenNashville, TN, Memphis, TN
  • Runner-up: Chattanooga, TN (beats all other candidates except the tied Condorcet winners)
  • Smallest margin: Nashville, TN over Chattanooga, TN (62-22; margin: 40)
  • Largest margin: Chattanooga, TN over Knoxville, TN (72-12; margin: 60)
  • Pairwise ties: 3
  • Total ballots: 84

Win-loss-tie (Condorcet/Copeland) table

TNexampleTie w-l-t table permalink:
🔗https://abif.electorama.com/id/TNexampleTie/pairwise#wlt
A modified version of the Tennessee example which demonstrates an IRV tie pairwise matchups
Nashville, TN
(2-0-2)
Nashville, TN
0 losses / 2 victories†
Chattanooga, TN
(1-1-2)
Nashville, TN: 62(73.8%)
Chattanooga, TN: 22(26.2%)
(No preference: 0; 0.0%)
Chattanooga, TN
1 loss / 1 victory†
Memphis, TN
(0-0-6)
Nashville, TN: 42(50.0%)
Memphis, TN: 42(50.0%)†
(No preference: 0; 0.0%)
Chattanooga, TN: 42(50.0%)
Memphis, TN: 42(50.0%)†
(No preference: 0; 0.0%)
Memphis, TN
0 losses / 0 victories†
Knoxville, TN
(0-2-2)
Nashville, TN: 62(73.8%)
Knoxville, TN: 22(26.2%)
(No preference: 0; 0.0%)
Chattanooga, TN: 72(85.7%)
Knoxville, TN: 12(14.3%)
(No preference: 0; 0.0%)
Memphis, TN: 42(50.0%)
Knoxville, TN: 42(50.0%)†
(No preference: 0; 0.0%)
† "Victories" and "losses" sometimes aren't displayed in the expected location when there are ties and/or cycles in the results, but the numbers provided should be accurate.

Pairwise tournament (Copeland ordered)

TNexampleTie pairwise diagram permalink:
🔗https://abif.electorama.com/id/TNexampleTie/pairwise#dot

%3 Nash Nash 2-0-2 (2 wins, 0 losses, 2 ties) Chat Chat 1-1-2 Nash->Chat ← Nash: 62 Chat: 22 Memph Memph 0-0-6 Nash->Memph ← Nash: 42 Memph: 42 Knox Knox 0-2-2 Nash->Knox ← Nash: 62 Knox: 22 Chat->Memph ← Chat: 42 Memph: 42 Chat->Knox ← Chat: 72 Knox: 12 Memph->Nash ← Memph: 42 Nash: 42 Memph->Chat ← Memph: 42 Chat: 42 Memph->Knox ← Memph: 42 Knox: 42 Knox->Memph ← Knox: 42 Memph: 42

Voting methods: FPTP • approval • IRV • STAR • Pairwise • All methods

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