The Math Behind Fiftis
How your group's percentage votes turn into a collective decision — no black box, just arithmetic.
The core formula
Each voter distributes 100 percentage points across all options. Fiftis computes the arithmetic mean for each option across all votes. The option with the highest average wins.
score(option) = (1 / n) × Σᵢ vᵢ(option)
- —n = total number of voters
- —vᵢ(option) = percentage voter i assigned to this option
- —Σᵢ = sum over all voters i
Since every voter distributes exactly 100 points, the sum of all score() values is always exactly 100%.
A worked example
3 voters, 3 options, 1 clear result.
| Voter | Italy | Spain | Greece |
|---|---|---|---|
| Anna | 60% | 30% | 10% |
| Ben | 20% | 50% | 30% |
| Clara | 40% | 40% | 20% |
| Average | 40%★ | 40%★ | 20% |
Italy and Spain tie at 40%. Fiftis shows this as a tie — your group can then discuss the two frontrunners knowing Greece is out.
Why not just use majority voting?
Plurality voting (pick one) discards intensity. If Anna strongly prefers Italy but Ben and Clara are mildly OK with Spain, Spain wins — even though Italy produces more total happiness. Percentage voting captures that gradient.
Plurality vote
Spain wins (2 vs 1 vote)
Ignores Anna's strong preference
Fiftis vote
Italy = Spain (40% each)
Shows the real tie — prompts discussion
How sliders stay summed to 100%
The constraint algorithm runs whenever a slider moves:
- 1Track which sliders the user has manually set ('locked').
- 2When slider i moves to value v: compute remaining = 100 − v − sum(locked sliders excluding i).
- 3Distribute remaining equally among all unlocked sliders.
- 4If all sliders are locked, reset the locked set to just {i} and redistribute.
- 5Fix rounding: add/subtract 1% from the last free slider to ensure the total is exactly 100%.
Fairness properties
Anonymity
The result doesn't change if you rename the voters — only values matter.
Unanimity
If all voters assign 100% to one option, that option wins with 100% average.
Continuity
A small change in preferences produces a small change in the result — no cliff-edges.
Equal weight
Every voter's 100 points counts equally. No HiPPO effect.
What Fiftis doesn't solve
No aggregation method is perfect (Arrow's impossibility theorem guarantees it). Fiftis doesn't weight voters by expertise, doesn't handle strategic voting resistance, and ties require a separate tiebreak. For most friend-group decisions, none of this matters — but now you know.