Comparing Single Winner Voting Systems

Disclaimer: There is no perfect single-winner voting system, and the hunt for one is like a quicksand for the mind. Instead, take a step back and reconsider why we even use single-winner system especially in the context of legislative assemblies where proportional representation would better address the core concern of unfair representation. Investigating systems that result in a low Gallagher Index are likely a better use of your time.

Step 1. Click each button to get descriptions of different ways one can compare single-winner voting systems.

Step 2. Drag and drop the criteria above into the order you consider most important to least.

Sort:
	Majority	Maj. loser	Mutual maj.	Condorcet	Cond. loser	Smith/ ISDA	LIIA	IIA	Cloneproof	Monotone	Consistency	Participation	Reversal symmetry	Polytime	Resolvable	Summable	Later-no-Harm	Later-no-Help	No favorite betrayal	Ballot type	Ranks
	Majority	Maj. loser	Mutual maj.	Condorcet	Cond. loser	Smith/ ISDA	LIIA	IIA	Cloneproof	Monotone	Consistency	Participation	Reversal symmetry	Polytime	Resolvable	Summable	Later-no-Harm	Later-no-Help	No favorite betrayal	Ballot type	Harm	Help	=	>2
Approval	Rated^[a]	No	No	No^[b]^[c]	No	No^[b]	Yes	Yes^[d]	Yes^[e]	Yes	Yes	Yes	Yes	O(N)	Yes	O(N)	No	Yes^[f]	Yes	Approvals	Yes	No
Borda count	No	Yes	No	No^[b]	Yes	No	No	No	Teams	Yes	Yes	Yes	Yes	O(N)	Yes	O(N)	No	Yes	No	Ranking	No	Yes
Copeland	Yes	Yes	Yes	Yes	Yes	Yes	No	No^[b]	Teams, crowds	Yes	No^[b]	No^[b]	Yes	O(N²)	No	O(N²)	No^[b]	No	No^[b]	Ranking	Yes	Yes
IRV (AV)	Yes	Yes	Yes	No^[b]	Yes	No^[b]	No	No	Yes	No	No	No	No	O(N²)	Yes^[g]	O(N!)^[h]	Yes	Yes	No	Ranking	No	Yes
Kemeny–Young	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No^[b]	Spoilers	Yes	No^[b] ^[i]	No^[b]	Yes	O(N!)	Yes	O(N²)^[j]	No^[b]	No	No^[b]	Ranking	Yes	Yes
Majority judgment^[k]	Rated^[l]	Yes^[m]	No^[n]	No^[b]^[c]	No	No^[b]	Yes	Yes^[d]	Yes	Yes	No^[o]	No^[p]	Depends^[q]	O(N)	Yes	O(N)^[r]	No^[s]	Yes	Yes	Scores^[t]	Yes	Yes
Minimax	Yes	No	No	Yes^[u]	No	No	No	No^[b]	Spoilers	Yes	No^[b]	No^[b]	No	O(N²)	Yes	O(N²)	No^[b]^[u]	No	No^[b]	Ranking	Yes	Yes
Plurality	Yes	No	No	No^[b]	No	No^[b]	No	No	Spoilers	Yes	Yes	Yes	No	O(N)	Yes	O(N)	N/A^[v]	N/A^[v]	No	Single mark	N/A	No
Range voting	No	No	No	No^[b]^[c]	No	No^[b]	Yes	Yes^[d]	Yes	Yes	Yes	Yes	Yes	O(N)	Yes	O(N)	No	Yes	Yes	Scores	Yes	Yes
Ranked pairs	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No^[b]	Yes	Yes	No^[b]	No^[p]^[b]	Yes	O(N⁴)	Yes	O(N²)	No^[b]	No	No^[p]^[b]	Ranking	Yes	Yes
Runoff voting	Yes	Yes	No	No^[b]	Yes	No^[b]	No	No	Spoilers	No	No	No	No	O(N)^[w]	Yes	O(N)^[w]	Yes	Yes^[x]	No	Single mark	N/A	No^[y]
Schulze	Yes	Yes	Yes	Yes	Yes	Yes	No	No^[b]	Yes	Yes	No^[b]	No^[p]^[b]	Yes	O(N³)	Yes	O(N²)	No^[b]	No	No^[p]^[b]	Ranking	Yes	Yes
Sortition, arbitrary winner^[z]	No	No	No	No^[b]	No	No^[b]	Yes	Yes	No	Yes	Yes	Yes	Yes	O(1)	No	O(1)	Yes	Yes	Yes	None	N/A	N/A
Random ballot^[aa]	No	No	No	No^[b]	No	No^[b]	Yes	Yes	Yes	Yes	Yes	Yes	Yes	O(N)	No	O(N)	Yes	Yes	Yes	Single mark	N/A	No