From Copilot: [bLOCKQUOTE]Here’s the crux: with the info you’ve given, the exact number of voters isn’t uniquely determined—but we can tightly bound it and still answer the percentage questions. Step 1: Tally and known ballots Total selections: 17 Option counts: Benny Agbayani: 4 Wally Backman: 2 Armando Benitez: 2 Ken Boswell: 2 Hubie Brooks: 5 None of the above: 2 Everyone else: 0 Known individual ballots: Voter A (Brooks-only): Brooks Voter B (you): Benitez, Agbayani, Brooks Voter C: None of the above Voter D: None of the above So far: Voters accounted for: 4 Selections accounted for: 1 + 3 + 1 + 1 = 6 Selections remaining: 17 − 6 = 11 Remaining counts to be supplied by unknown voters: Agbayani: 3 Backman: 2 Benitez: 1 Boswell: 2 Brooks: 3 Step 2: Possible number of voters Each voter can choose between 1 and 5 options. Remaining selections: 11 Minimum additional voters: ⌈ 11 / 5 ⌉ = 3 Example feasible pattern: three voters with 5, 4, and 2 picks respectively (you can assign them to match the remaining counts without conflict). Maximum additional voters: 11 (if each of those 11 selections is from a different single-choice voter). So: Total voters 𝑁 is between: 4 + 3 = 7 and 4 + 11 = 15 i.e. 7 ≤ 𝑁 ≤ 15 We cannot pin down a unique 𝑁 from the given data. Step 3: Who received at least 75% of the vote? To get at least 75% of the voters, a candidate must be chosen by at least 0.75 𝑁 distinct voters. The maximum possible support for any candidate is bounded by their total selections: Hubie Brooks: 5 selections → at most 5 distinct voters Others have ≤4 selections Given 7 ≤ 𝑁 ≤ 15 : Max possible fraction for Brooks: 5 7 ≈ 71.4 % < 75 % For larger 𝑁 , the fraction only decreases. So: No candidate can possibly reach 75% of the voters. Answer: Nobody received at least 75% of the vote. Step 4: Who received at least 5% of the vote? Now we look for candidates who definitely have ≥5% of the voters, for any feasible 𝑁 in [ 7 , 15 ] . A candidate with at least 1 selection is supported by at least 1 voter. The worst case (smallest fraction) is when 𝑁 is largest: 𝑁 = 15 . Then: 1 15 ≈ 6.7 % > 5 % So anyone with at least 1 selection necessarily has ≥5% of the voters, regardless of the exact 𝑁 in the allowed range. Those are: Benny Agbayani (4) Wally Backman (2) Armando Benitez (2) Ken Boswell (2) Hubie Brooks (5) None of the above (2) Everyone else has 0 and thus 0%. Direct answers Who received at least 75% of the vote? No one. Who received at least 5% of the vote? Agbayani, Backman, Benitez, Boswell, Brooks, and “None of the above”. How many total voters were there? Not uniquely determined; the total number of voters is between 7 and 15 inclusive.[/bLOCKQUOTE] And from Grok: [bLOCKQUOTE]No one received at least 75% of the vote. The candidates who received at least 5% of the vote are Benny Agbayani, Wally Backman, Armando Benitez, Ken Boswell, and Hubie Brooks (all others at 0%). The percentages are relative to the number of voters (ballots), not total selections. This is the standard way "percentage of the vote" is interpreted in multi-select limited-choice voting systems (e.g., Hall of Fame-style ballots where voters select up to 5, and thresholds like 75% refer to share of ballots received). The data's listed percentages (e.g., 29% for Brooks = 5/17) are instead share of total selections, which is a different (and less common for thresholds) metric. The total number of voters cannot be uniquely determined from the given information, but there are constraints: Minimum voters: 7 (the fewest possible consistent with the rules, vote counts, one single-player Brooks voter, two "none of the above" voters, your 3-vote ballot, max 5 per voter, and no other single-player voters for any candidate). This uses maximal bundling of the remaining 11 votes into 3 efficient multi-selection ballots (as in one with 5, one with 4, one with 2—all including Agbayani + Brooks to cover their high remaining counts). Maximum voters: Fewer than 17 (since some voted multiple), but more precisely up to around 13–15 depending on how much splitting is possible without creating forbidden extra single-player ballots. Since the number of voters is at least 7, the maximum possible approval percentage any candidate can have is 5/7 ≈ 71.4% (Hubie Brooks). No candidate reaches 75% in any possible configuration (larger voter counts would only decrease the percentages further). For the 5% threshold (at least 0.05 × voters): In the minimal case (7 voters), 5% = 0.35 → any candidate with ≥1 vote has at least 1/7 ≈ 14.3% > 5%. In larger cases (higher voters), percentages drop, but even in the highest plausible voter counts, the candidates with votes still clear 5% (Brooks with 5 votes would need >100 voters to drop below 5%, impossible given only 17 total selections). Thus, the same five candidates who got any votes at all meet ≥5% in all possible cases. Summary: ≥75%: No one. ≥5%: Benny Agbayani, Wally Backman, Armando Benitez, Ken Boswell, Hubie Brooks. Total voters: Unknown exactly, but at least 7 (most likely 7 if assuming efficient / minimal-voter configuration typical in such logic problems).[/bLOCKQUOTE] The more data we get and the more people that post who they vote (or don't vote) for will provide more givens which can allow for greater clarity later on. (or I could just switch to an external polling source that uses more traditional tabulation methods). We could theoretically do it without a poll and just have people post their individual lists, but having done this project for ~15 years or so on the other website, I found that that slightly more effort-demanding step limits participation a bit.