Voting

Score ranked ballots with plurality, Borda, and Schulze

Add ballots with a count and ranked candidate order. Use plain sequences like BACD or explicit ties / ranking gaps like A=B>C=D. Invalid ballots stay visible but are excluded from scoring.

Ballots

Add weighted ranked ballots before reviewing the score output.

CountPreference orderAction

4

Ballots entered

4

Valid ballots

12

Weighted votes

Input notes

Simple ranking

ABCD means A over B over C over D.

Ties

A=B>C=D means A tied with B, both ahead of C tied with D.

Skipped candidates

Missing candidates are treated as being below listed candidates in pairwise comparisons.

Results

Schulze method results

Candidates: A, B, C, D

Rank 1

B

Pairwise wins: 3

Rank 2

A

Pairwise wins: 2

Rank 3

C

Pairwise wins: 1

Rank 4

D

Pairwise wins: 0

Ballot summary

BallotCount
BACD7
CADB2
DACB2
ACDB1

Rank-order centroid

Position 10.5208
Position 20.2708
Position 30.1458
Position 40.0625

Pairwise wins

CandidateABCD
A051010
B7077
C25010
D2520

Schulze path strengths

CandidateABCD
A001010
B7077
C00010
D0000

References

Voting system summaries, strengths, and weaknesses

These notes summarize the corresponding Wikipedia pages for the three methods implemented above and call out the tradeoffs most relevant to this tool.

Plurality voting

Plurality elects the candidate with more votes than any other candidate, even when that total is not a majority. It is the simplest of the three methods here because each ballot effectively contributes only to its top-ranked option.

Wikipedia

Strengths

  • Very simple ballot design and counting process.
  • Easy to explain to voters and stakeholders.
  • Fast to tally and operationally cheap to administer.

Weaknesses

  • A candidate can win without majority support.
  • Wikipedia highlights wasted votes, tactical voting, and spoiler effects as common issues.
  • Lower-ranked preferences are ignored, so consensus candidates can lose.

Borda count

Borda count is a positional ranked system: candidates receive points based on how many options they are ranked above, and the highest total wins. It tends to reward broad acceptability instead of only first-choice intensity.

Wikipedia

Strengths

  • Uses the full ranking instead of only the top choice.
  • Often favors broadly acceptable candidates over polarizing ones.
  • Straightforward point-based calculation once rankings are collected.

Weaknesses

  • Wikipedia notes it is easy to manipulate strategically.
  • Results can be sensitive to nomination effects and similar candidates on the ballot.
  • A majority-preferred candidate is not guaranteed to win.

Schulze method

The Schulze method is a Condorcet completion rule that compares candidates pairwise and resolves cycles using strongest paths, also called beatpaths. If there is a candidate who would beat every other candidate head-to-head, Schulze will elect that candidate.

Wikipedia

Strengths

  • Condorcet-consistent when a head-to-head winner exists.
  • Wikipedia lists strong theoretical properties including monotonicity, clone independence, and the Smith criterion.
  • Uses pairwise comparisons, which usually aligns better with majority preferences in ranked elections.

Weaknesses

  • Harder to explain and audit informally than plurality or Borda.
  • Requires pairwise matrix and path-strength calculations, which increases implementation complexity.
  • Tie handling and interpretation of equal rankings add design choices that need to be made explicitly.