Simple example (Tennessee capitol)

🔗 TNexample (tags: { theoretical , CondorcetVsIRV , CenterSqueeze , featured })

Below is the ABIF from the "TNexample" election (Simple example (Tennessee capitol))

ABIF submission area (show)

Method options

FPTP results?

IRV/RCV results?

IRV extra analysis?

Approval results?

STAR results?

pairwise (Condorcet/Copeland) results?

pairwise tournament diagram?

Ballot options Transform ballots (using ballot-type metadata)?

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

Results

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

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 "ranked". 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
IRV/RCV	Knox
FPTP	Memph
Approval	Nash
STAR	Nash
Condorcet/Copeland	Nash

OFF ON tabbed view

IRV/RCV results

TNexample IRV/RCV result permalink:
🔗https://abif.electorama.com/id/TNexample/IRV#IRV

IRV/RCV Winner: Knox with 58 votes (58.0%) in final round
Runner-up: Memph 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%)
Memph: 42 (42.0%) →	Memph: 42 (42.0%) →	Memph: 42 (42.0%) (🛑eliminated) →
Nash: 26 (26.0%) →	Nash: 26 (26.0%) (🛑eliminated) →	~~Nash~~
Knox: 17 (17.0%) →	Knox: 32 (32.0%) →	IRV/RCV winner: Knox: 58 (58.0%)✅ →
Chat: 15 (15.0%) (🛑eliminated) →	~~Chat~~	~~Chat~~

FPTP result

"FPTP" is "First-past-the-post", also known as "plurality" or "choose-one"
TNexample FPTP results permalink:
🔗https://abif.electorama.com/id/TNexample/FPTP#FPTP

FPTP Winner: Memph with 42 first-place votes (42.0%)
Runner-up: Nash with 26 first-place votes (26.0%)
Margin of victory: 16 votes (16.0 percentage points)
First-place votes
- Memph: 42 votes (42.0 %)
- Nash: 26 votes (26.0 %)
- Knox: 17 votes (17.0 %)
- Chat: 15 votes (15.0 %)
Total ballots: 100

Approval voting results

TNexample approval voting results permalink:
🔗https://abif.electorama.com/id/TNexample/approval#approval

📝

Note — Approval counts estimated from 100 ranked 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: Memph, Nash, and Knox. 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 ranked ballots.

Conversion method: favorite_viable_half

#------- metadata -------
{ballotcount: 100}
{is_ranking_to_rating: true}
#------ candlines ------
=Memph:[Memph]
=Nash:[Nash]
=Chat:[Chat]
=Knox:[Knox]
#------- 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: Nash
Approval Results:
- Nash — 100 approvals (100.0% of ballots) (✅ winner)
- Chat — 58 approvals (58.0% of ballots)
- Knox — 58 approvals (58.0% of ballots)
- Memph — 42 approvals (42.0% of ballots)
Total: 100 ballots (258 total approvals)

STAR results

TNexample STAR results permalink:
🔗https://abif.electorama.com/id/TNexample/STAR#STAR

📝

Note — STAR ratings estimated from ranked ballots using Borda scoring method

Details

The ranked ballots have been converted to STAR ratings using Borda scoring: each candidate receives points equal to (number_of_candidates - their_rank). In this election, we have 4 candidates, so the 1st choice gets 3 points, the 2nd choice gets 2 points, etc. These Borda scores are then used as STAR ratings for tabulation by STAR.

STAR winner: Nash
Finalists: Nash vs Chat
Runoff result:
- Nash: 68 votes (68.0%)
- Chat: 32 votes (32.0%)
- No preference: 0 voters (0.0%)
Total stars allocated: 600
Total ballots: 100

★★★★★★

★★★★★

★★★★★★

★★★★★

★★★★★★

★★★★★

★★★★★★

★★★★★

★★★★★★

(one star above is approximately 12 stars allocated by voters)

First round:
- ★#0: Nash received 194 stars (32.3%) from 100 voters (100.0%)
- ★#1: Chat received 173 stars (28.8%) from 100 voters (100.0%)
- ★#2: Memph received 126 stars (21.0%) from 42 voters (42.0%)
- ★#3: Knox received 107 stars (17.8%) from 58 voters (58.0%)
Finalists:
- ★Nash (✅ winner) preferred by 68 of 100 voters
- ★Chat preferred by 32 of 100 voters
- ★No preference between the finalists: 0

NOTE: Since ratings or stars are not present in the provided ballots, allocated stars are estimated using a Borda-like formula.

Condorcet/Copeland results

TNexample Condorcet/Copeland results permalink:
🔗https://abif.electorama.com/id/TNexample/pairwise#pairwise

Winner: Nash
Runner-up: Chat (beats all other candidates except Nash)
Smallest margin: Nash over Memph (58-42; margin: 16)
Largest margin: Chat over Knox (83-17; margin: 66)
Pairwise ties: none
Total ballots: 100

Win-loss-tie (Condorcet/Copeland) table

TNexample w-l-t table permalink:
🔗https://abif.electorama.com/id/TNexample/pairwise#wlt

Simple example (Tennessee capitol) pairwise matchups
Nash (3-0-0)	Nash 3 victories ⇣
Chat (2-1-0)	Nash: 68(68.0%) Chat: 32(32.0%) (No preference: 0; 0.0%)	Chat ⇽ 1 loss / 2 victories^† ⇣
Knox (1-2-0)	Nash: 68(68.0%) Knox: 32(32.0%) (No preference: 0; 0.0%)	Chat: 83(83.0%) Knox: 17(17.0%) (No preference: 0; 0.0%)	Knox ⇽ 2 losses / 1 victory^† ⇣
Memph (0-3-0)	Nash: 58(58.0%) Memph: 42(42.0%) (No preference: 0; 0.0%)	Chat: 58(58.0%) Memph: 42(42.0%) (No preference: 0; 0.0%)	Knox: 58(58.0%) Memph: 42(42.0%) (No preference: 0; 0.0%)

Pairwise tournament (Copeland ordered)

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

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

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