Data Representation¶
In preferential or ranked voting, each voter expresses an ordered list of preferences over a set of candidates. When representing this data in tabular form, there are multiple valid approaches, each suited to different kinds of analysis.
Let's assume there are 4 candidates: A, B, C, and D.
Ranking Position as Columns¶
One common approach is to use a "ranking-position as column" format. In this structure, each row represents a voter, and each column corresponds to a ranking position ( e.g. first, second, third). The cell values indicate the candidate ranked at that position. This format directly shows each voter's preference order.
| count | rank_1 | rank_2 | rank_3 | rank_4 |
|---|---|---|---|---|
| C | A | B | D | |
Appropriate use cases:
- Implementing ranked voting rules such as Instant Runoff, Borda Count, or Top-k approval.
- Identifying the top-ranked candidate per voter.
- Grouping or counting identical ballots.
- Working with data that mirrors the structure of actual ballots.
Limitations:
- It is less efficient for analyses that require identifying the rank assigned to a specific candidate without reshaping the data.
Candidate as Columns¶
An alternative approach is the "candidate as column" format, where each row also represents a voter, but each column corresponds to a candidate, and the cell values indicate the rank assigned to that candidate by the voter. This format makes it easy to compare how each candidate was ranked across voters.
| count | A | B | C | D |
|---|---|---|---|---|
| 1 | 2 | 0 | 3 | |
Appropriate use cases:
- Analyzing rankings from the perspective of each candidate (e.g., average or median rank).
- Performing pairwise comparisons used in Condorcet methods.
- Computing how frequently a specific candidate appears in a given rank.
- Applying statistical or machine learning models where candidates are treated as variables.
Limitations:
- It may require reshaping the data to apply position-based voting rules.
Comparison¶
Choosing the right tabular format for ranked voting data depends on the task.
| Task | Recommended Format |
|---|---|
| Implementing ranked-choice voting rules | Ranking position as columns |
| Counting first-choice votes | Ranking position as columns |
| Computing statistics per candidate | Candidate as columns |
| Analyzing pairwise comparisons (Condorcet) | Candidate as columns |
| Grouping or aggregating identical ballots | Ranking position as columns |
| Applying statistical models to ranking data | Candidate as columns |