Puzzles
range from "easy" to "so hard nobody can currently solve them" (i.e. "open");
we've taken pity on you by giving a very-subjective
"difficulty level" from [0] to [9].
If you can solve one of the
**open [9]** problems please let warren.wds at gmail.com know!
[You can also contribute new puzzles to him...]

For **terminology**, it may help to consult our glossary.
"Range Voting" will generally mean "continuum range voting" and *not*
range voting with scores restricted to the discrete set {0,1,...,99} for
mathematical analysis purposes.

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Puzzle answers only available to those who know the password, i.e, CRV members!
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#0 (Voting power – ultra-easy speed problem)[0]

#1: The minimum it takes to elect US president[1]

#2: Small elections in which many voting systems all disagree[5]

#3 (interesting – easy once you see it, otherwise hard!)[4]

#4: Non-monotonicity probabilities in IRV voting[6]

#5 (~~open~~ Now solved! – voting systems obeying both ICC and AFB)[7]

#6: Dice[2]

#7: Probabilities of "Condorcet cycles."

#9 (~~open~~ Now solved! – voting systems in which semi-honest voting is strategic)

#12 (cutting of 2-dimensional cakes)

#13 (range-voting with outlier-discarding)

#14 (mostly open – Social science/economics research. Suggested by Aaron Krowne)

#15 (~~open~~ Now solved! – multiwinner EP & PR voting systems)

#16 (Raising the mean of both sets by shuffling them – easy)

#17 – Probability of "Peru scenario"[6]

#18 – IRV refuses to elect a candidate who beats every other pairwise by 99:1 margin?

#19 – A situation with random other voters where your strategically best range vote is honest.

#22 – How bad can Condorcet cycles be? [7]

#23 – Avoiding favorite-betrayal (Chris Benham)

#24 – What is the probability plurality elects the candidate a majority least-likes?

#26 – Super-bad tournaments[5]

#27 – A quantity like the "Ramsey numbers" but defined for directed rather than undirected graphs.

#28 – How many votes suffice to create any "tournament" configuration?[8]

#30 – Election where Borda and Approval voting maximally disagree. [2]

#31 – Election where Borda reverses [2]

#32 – The "Three Stooges voting problem" (Alan Frieze)

#33 – Wisest allocation of vote-weights

#34 – How much ignoring does Instant Runoff Voting do?

#35 – Gerrymandering cancellation theorem

#41: Invisibly Corrupted Computer Programs.

#42: Probability of Condorcet cycle

#43: Approval voting strategy most likely to elect Condorcet winner

#44: Shannon Utility Honesty property

#45: (Open) Min-Max matrix product

#46: Probability of unclear election winners

#47: "Vote for N" leading to unclear election winners

#48: How many votes to count to get confidence?

#49: Machievellian Agenda Manipulation

#50: How many checks to get confidence?

#51: Getting true (not fake) randomness

#52: How many votes to count to get 100% certainty of winner?

#53: Districting is unavoidably "chaotic"

#55: How often is voting honestly worse than not voting with Instant Runoff Voting?

#56: How often is voting honestly worse than not voting (with Condorcet)?

#57: How often is dishonesty better strategy than honesty with IRV?

#59: Gerrymandering "Squareland"

#60: Range and Approval as "universal" voting systems

#61: Voting system "stability" (S.J.Brams)

#62: How often is dishonesty better strategy than honesty with Condorcet?

#63: Optimal size for a legislature [2]

#64: Expected number of votes counted before certain [6]

#65: Partitioning squareland into some nice patterns [4]

#66: Optimal Districting – least cutting [8]

#67: Dice can do damned near anything? [7]

#69: Optimal way to form a "coalition" [3]

#70: "Marriages" and "Capitalism." [5]

#71: The impossibility of districting into squares & triangles [6]

#73: Manipulation of most reasonable voting methods is easy [6]

#74: How bad can "Shortest Splitline" districts be? [4]

#75: Monty Hall problem (famously tricky probability puzzle) [2]

#77: Learning how to play games [8]

#78: Florida counties' biased enforcement of rules for overseas ballots in 2000 [4]

#79: Biased purging in Ohio 2004 [3]

#80: Biased Voter turnout in Lucas County Ohio 2004 [3]

#81: Hierarchical government [5]

#84: Optimum districting longer for larger country? [1]

#85: Condorcet cycle probability (Dirichlet model)? [5]

#86: Copeland is comparatively good with strategic voters? [5]

#87 Generalized "Monty Hall" probability puzzles [2]

#88 "Optimum" voting system maximizing chance of Condorcet winner [8]

#89 Probability of Majority-top winner in Dirichlet election [4]

#90 Burial works in Condorcet voting [3]

#91 Number of count-types to publicize [3]

#92 Permit cycles in Condorcet ballots? [3]

#94: The "YN model" – a simple voting model [7]

#96 Human "happiness" and Darwinian evolution [2]

#97 "Allais Paradox" for utilities [2]

#98 Random Sampling of a Subset [4]

#99 Efficient generation of correct "random election" pair-margins matrices [6]

#100 Copeland Tie Probability and Behavior [6]

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