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I remember the Schulze Method from back when I was studying Econ... that was years ago and my math isn't the greatest, go easy on me.

We are piloting a project to make a to-do list app for teams, I'm looking for a voting, ranking method to rank many, many items, across many people and I'm not math-savvy enough to choose a ranking method. This might be feature requests for our product.

I'm investigating a system whereby the team (team A) could come up with items to-do: A1, A2, A3. The members of Team A, lets say TA1, TA2... TA5 all vote in a "hot or not" style. That can give me the pairwise ranking for each player in that team. An order of what's important.

Question 1 - can Schulze method create an ordered rank of preferences, even if player TA5 doesn't complete all their possible rankings?

In parallel, team B creates their own to-dos. Slogans B1, B2, B3. Repeat the same method as above.

Question 2a - can Schulze method give an ordered ranking of B1,B2,B3 and A1,A2,A3. and what conditions are there (i'm assuming you'd need at least one pair-wise ranking from set A and set B). Lets assume a third team, C (for CEO) can cast a few votes, create a pairwise preference.

Question 2b - Would it matter that the CEO only casts a few votes?

Question 3 - What considerations to the model would I have to make if looking to implement a system where anyone can add "to-do's" and vote on "to-dos". Imagine a company-wide feature request system. Anyone can add a feature e.g. "Ability to make coffee". Anyone can dip into this fantasy system and "hot vs not" ideas, the best ideas float to the surface. Is Schulze the best method?

I'd love to hear comments and solutions, I'm at a total loss!

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There is lots of information about different voting systems and their properties from an axiomatic point of view here: http://rangevoting.org/ One can force voters to use "untruncated" ballots or one can allow that. There is also a discussion of different types of ballots that can be used.

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vote in a "hot or not" style

Hot or Not is ratings, not rankings.

to rank many, many items

For one person to rank all items all at once is very difficult, and many of the ranks produced will be meaningless.

To rate them (give them 1-5 stars, for instance) is easier, and will produce good results if averaged "across many people", but still time-consuming. The algorithm is much simpler than Condorcet, though: Just average the scores for a given candidate.

A better method might be to do many pairwise comparisons and try to estimate their utility using something like Elo ratings? Better yet, the "Glicko" method includes an estimate of the accuracy of the results, so you can prioritize comparisons between the candidates for which there is the most uncertainty.

This assumes that all of the candidates exist along a single dimension of preference, though, which is not generally true.

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