Past riddles

To join, you will need a password, which is a 9-letter all-lowercase word. It is used when saying "this alternative got more votes than any other alternative (even if may not have majority support), so it has _________ support". It is also the name of the unique scoring rule where the winning alternatives do not change after we remove a Pareto-dominated alternative from the preference profile (Richelson 1978).


To join, you will need a password, which is a 5-letter all-lowercase word which is the surname of the first person to work on social choice theory (truly an oldie but goodie!). The word also refers to a shape which is used to point people the right way; this shape can be obtained by writing a minus followed by a greater-than sign.


To join, you will need a password, which is of form word9 where

  • the all-lowercase five-letter word completes "round _____" which is an allocation rule where agents sit in a circle and then take turns choosing their favourite untaken item. The word also describes a bird with a red breast, and it is the first name of Mr. Hood who is known for stealing from the rich to give to the poor.

  • the number between 0 and 4 describes how many of the following indices are power indices which can be used to analyze weighted voting:

    • S&P 500 index

    • Shapley-Shubik index

    • h-index

    • Penrose-Banzhaf index


To join you will need a password, which is of form letters9 where

  • there are exactly five letters that complete the word gerry______ing which is a word describing strategic redistricting to win more seats in parliamentary elections. Also, a com______ is someone who tells others what to do.

  • the digit describes the maximum probability that one can possibly assign an event. It also solves the equation 5x = 5.


To obtain the link to today's seminar, you need to solve a quiz. (You should answer at least one out of three questions correctly.) To avoid the quiz, sign up for our email list, where you can get the link for free!


To obtain the link to today's seminar, you need to solve a riddle, which you can find here.


The password is of the form "word9" (an all-lowercase word followed by a single digit).

  • The four-letter word is the name of the town housing the offices of the Society for Social Choice and Welfare.

  • The digit is the odd one out: (1) anonymity, (2) efficiency, (3) monotonicity, (4) neutrality, (5) proportionality, (6) safety, (7) strategyproofness.


To join, you will need a password, which is of form word12 where

  • the seven-letter word is the correct answer: "the set of stable matchings forms a _______, so it is closed under the ∧ and ∨ operations" (it's the term for a poset with unique supremums and infimums; the word sounds a lot like lettuce but is spelled differently)

  • the two digit number is the answer: "in order to have an h-index of 5, what is the minimum number of citations your papers must have received combined?"


To join, you will need a password, which is of form word9 where

  • the 4-letter word is the name of a trading cycle of length 2 (in house allocation, agents in a trading cycle pass on their house to the next agent in the cycle, making every cycle member better off)

  • the digit is the maximum number of alternatives that can be selected as winning by a resolute voting rule in a given preference profile


To join, you will need a password, which is of form word9, where

  • the three-letter abbreviated word completes "to deterministically check whether a given value occurs in a sorted list of length n, the best algorithm requires O(___ n) comparison queries". The word is short for ___agrithm.

  • the digit is the correct answer: When talking about possible and necessary winners, the term "possible" most closely corresponds to which symbol? (1) ⊆ (2) ¬ (3) ∨ (4) ∃ (5) ∅ (6) + (7) ∉ (8) ε (9) ℚ


To join, you will need a password. To celebrate our 1-year anniversary 🥳, the password is identical to our very first password, which was determined in unusual haste while under attack. It is the last names of the two inventors of the deferred acceptance mechanism for stable marriage, written in lower-case letters without a space or hyphen. Because zoom (still!) limits passwords to 10 characters, you need to omit the final letter "y". For example, if the inventors had been named Gauss and Cayley, the password would be "gausscayle".


The password is of the form "word9" (an all-lowercase word followed by a single digit).

  • The seven-letter word completes the sentence "a vector of preferences, one for each voter, is also known as a preference _________".

  • The digit is the correct completion: amongst matching theorists, Boston is famous for its (1) Marathon, (2) Massacre, (3) Market, (4) Mechanism, (5) Mural, (6) Museum.


To join, you will need a password which is of form word9 where

  • the three-letter lower-case word is the name of the container commonly used in thought experiments in probability theory, where it typically contains balls of different colors.

  • the number is the median of the following numbers: 1 6 7 8 9.


To join, you will need a password, which is of form word9 where

  • the word completes: "a matching is ______ if there is no pair of agents each of whom prefers the other to their partner in the matching"

  • the digit is the smallest number of agents who can form a multi-agent system (it is also the unique positive integer with x^2 = 2x)


To join, you will need a password, which is of form word9, where

  • The four-letter lower-case word completes: "a Nash equilibrium in which all strategies are played with probability either 0 or 1 is called a ____ Nash equilibrium".

  • the digit is the correct answer: in the study of distortion, an omniscient mechanism with access to all information achieves distortion _. (The digit is also known as the multiplicative identity.)


The password is of the form "word9" (an all-lowercase word followed by a single digit).

  • The four-letter word completes this sentence: In voting theory, the antiplurality rule is also known as the ______ rule.

  • Borda's rule is intended for voters who are (1) at least 21 years of age, (2) strategic, (3) smart, (4) computer-savvy, (5) experienced, (6) honest, (7) French.


To join, you will need a password, which is of form word9, where

  • the word completes: "in ______ democracy, voters may delegate their vote." It is also an adjective often used to describe water.

  • the digit is the correct answer: which of these is a false statement about additive valuations? (1) they can be concisely represented (2) they allow voters to be indifferent between all bundles (3) they allow voters to express substitutes and complements (4) they are used on Spliddit (5) they are both submodular and supermodular (6) if non-negative, they are monotonic in the sense that a superset is weakly preferred (7) they make research easier


To join, you will need a password, which is of form word9 where

  • the five-letter lowercase word completes the sentence: "in transferable utility games, a player whose marginal contribution to all coalitions is 0 is known as a null player or _____ player". The word also refers to a puppet placed in cars during crash tests.

  • the digit is the correct answer: the cardinality of the powerset of a non-empty finite set is always (1) irrational (2) infinite (3) even (4) prime (5) perfect (6) taxicab (7) negative.


To join, you will need a password, which is of form word9, where

  • the lower-case five-letter word is the first name of the inventor of PageRank (note that it's not BrinRank)

  • the digit is the correct answer: d(x,z) <= d(x,y) + d(y,z) is known as (1) the xyz conjecture (2) Manhattan distance (3) Euler's formula (4) Gini coefficient (5) triangle inequality (6) Fermat's last theorem (7) commutativity


To join, you'll need a password, which is of form word9, where

  • the four-letter all-lowercase word is the last name of the inventor of the bargaining solution that involves multiplying utilities,

  • the digit is the correct answer: when analyzing approval voting, we often assume that preferences are... (1) irrational (2) dichotomous (3) hard to compute (4) transcendental (5) commutative (6) Hausdorff


To join, you will need a password, which is of form letters9, consisting of

  • six lower-case letters, which complete the sentence: "in fair division, an allocation is said to be ______tional if each agent gets utility at least 1/n times the utility of all available resources".

  • a digit, which is the correct answer: Who of these philosophers is most likely to refuse to lie to a murderer at their door? (1) Kant (2) Bentham (3) Sidgwick (4) Mill (5) Singer (6) Harsanyi


To join, you'll need a password which is of form word9, where

  • the five-letter lower-case word completes: "in a coalition formation game, the coalition consisting of all players is known as the _____ coalition". In slang, the word is also used to refer to 1,000 monetary units.

  • the digit is the correct answer: it is not usually possible to have a single-valued voting rule that is anonymous and neutral, because these properties sometimes force a (1) shirt (2) hat (3) jacket (4) gown (5) sock (6) tie (7) shoe


To join, you will need a password, which is of form word9, where

  • the 5-letter word completes: "if you elect a committee, or want to do participatory budgeting where all projects cost the same, you should use a _____-winner voting rule". (The answer is not "single".)

  • The digit is the correct answer: Suppose you have a transferable-utility game and impose additivity, symmetry, dummy, and efficiency on a real-valued function on the set of players. Then you get (1) Nash equilibrium (2) subgame perfect equilibrium (3) Shapley value (4) Condorcet winner (5) Borda rule (6) vNM utilities (7) indifference curves


To join, you will need a password, which is of form word9, where

  • the 9-letter lower-case word is the name of a borough of a major American city, which is often associated with the metric based on the ℓ_1 norm

  • the digit is the correct answer: Which country uses instant runoff voting to elect members of a national parliament? (1) Germany (2) USA (3) England (4) Poland (5) Australia (6) Israel (7) Netherlands (8) North Korea


To join, you will need a password, which is of form word9, where

  • the five-letter word completes: "a voting rule is strategy_____ if a voter cannot obtain a better outcome by reporting false preferences"

  • the digit is the number of different voting rules that satisfy the above property and are also resolute, non-dictatorial, and onto when there are 5 alternatives and 7 voters.


You will need a password, which is a 10-letter all-lowercase word, skipping the hyphen. It completes the sentence: "Sperner's lemma is often used to prove _____-_____ theorems. John Nash used one such theorem to prove the existence of equilibrium in games with mixed strategies."


You will need a password, which is of form word9, where

  • the word is the all-lowercase last name of someone who characterized a class of scoring rules in 1995, found a good choice of a reserve price for second-price auctions, won a prestigious Swedish memorial award, and wrote a textbook on game theory with a blue cover. (Remember, it's -son, not -sen.)

  • the digit is the correct answer: Someone else characterized a class of scoring rules, first the Borda rule in 1974, then all scoring rules in 1975, using the consistency axiom. He later wrote about Kemeny's rule. That person's last name is the opposite of: (1) small (2) old (3) happy (4) round (5) sunny (6) patriotic (7) stale. [Hint]


To join, you will need a password, which is of form word9, where

  • the word completes the sentence: "to prove that a dynamic process converges, a useful proof technique is a _________ function argument, where a bounded function is shown to increase with every iteration"

  • the digit is the correct answer: Which of these is a fairness notion? (1) APX (2) PSPACE (3) NASA (4) EF1 (5) POTUS (6) AAAI (7) CMT


The password is of the form “word9” (an all-lowercase word followed by a single digit).

  • The five-letter word completes the sentence “There are more people working on computational social choice living in _______ than in any other city in the world.”

  • The digit is the correct answer: Which acronym is not commonly found in papers on computational social choice? (1) EFX, (2) IIA, (3) PAV, (4) PSR, (5) SCF, (6) STV, (7) ZFC.


You will need a password, which is form word9, where:

  • the 8-letter lower-case word completes: "________ rule is the canonical voting rule for 2 alternatives; for odd number of voters it is resolute, anonymous, neutral, and monotonic."

  • The above voting rule is characterized by those axioms. This theorem is named after someone whose last name is naturally interpreted as a number between 1 and 12; in this case it's a single digit. [Hint: Econometrica, Vol. 20, Issue 4, pp. 680–684, 1952.]


To join, you will need a password, which is of the form word9, where

  • the word is the five-letter all-lowercase last name of the 1700s French innovator whose voting rule was intended only for "honest men",

  • the digit is the number of ways we can assign three houses to three agents, so that each agent receives exactly one house.


You will need a password to join, which is of the form word9, where

  • the nine-letter word starts in 'c', and completes "a hedonic game is a type of _________ formation game"; it also refers to a group of political parties formed to govern.

  • the digit is the correct answer: Which of these is a formula of propositional logic in conjunctive normal form?

  1. ∃x ∀y ¬ y ∈ x

  2. □p ↔ ¬◇¬p

  3. (x ∨ y ∨ ¬z) ∧ (¬ x ∨ z)

  4. x = (-b+-√b²-4ac) / 2a

  5. {∅, {∅}, {∅, {∅}}}

  6. e = mc²

  7. ɸ^d(ρ, σ)/((1+φ)(1+φ+φ²)⋅⋅⋅(1+⋅⋅⋅+φⁿ⁻¹))

  8. maxₓ minᵢ uᵢ(x)

  9. (α → (β → γ)) → ((α → β) → (α → γ))


To join, you will need a password, which is of the form word9, where

  • the word completes "backward _________", a method to compute a subgame-perfect equilibrium in sequential games

  • the digit is the answer: what do fair allocationists call the interval [0, 1]? (1) cute (2) open (3) disconnected (4) snake (5) cake (6) spaghetti (7) tofu


You will need a password, which is of the form word9, where

  • the all-lowercase word completes the name of the journal/society/conference, which is "social choice and _______",

  • the digit is the winner under approval voting applied to the profile {1, 2, 3}, {2}, {2, 3}, {1, 4}, {5, 6, 7, 8}.


You will need a password, which is of the form "word89", where

  • the word contains a double-o and completes the sentence: "A simple protocol to fairly divide a cake among two players is cut and ______."

  • the two-digit number is the number of ways you can rank 4 alternatives in a linear order (i.e., complete with no ties). It is also a thirtieth of the number of hours in June.


You will need a password, which is of the form "word9", where

  • the six-letter word completes the sentence: "a voting rule is often called an SCF, which is short for social ______ function"

  • the digit is the correct answer: Consider the three-voter preference profile with x >₁ y >₁ z and y >₂ z >₂ x and z >₃ x >₃ y. The main problem with this profile is that ...

  1. voter 2's preferences contain too many ties

  2. the Shapley value of this profile is irrational

  3. it is a counterexample to Arrow's Impossibility Theorem

  4. its pairwise majority relation is not transitive

  5. it has a unique Condorcet winner

  6. it is NP-complete under Turing reductions

  7. it is single-peaked

  8. its construction requires the axiom of choice


Hint: You will need to enter a password, which is of the form "word9", where

  • the seven-letter word starts in 'u' and completes the sentence: "For a preference relation ≻ over C, we say that u : C → ℝ is a _______ function representing ≻ if for all x, y ∈ C, we have u(x) > u(y) if and only if x ≻ y." The same word completes the sentence: "To satisfy the von Neumann--Morgenstern axioms, you must maximize expected _______."

  • the digit is the correct answer: Who proved an impossibility theorem? (1) square, (2) triangle, (3) line, (4) curve, (5) arrow, (6) rectangle, (7) parallelogram, (8) circle


You will need to enter a password to join. The password is of the form “word9”, where:

  • The nine-letter word completes the sentence: “If an alternative is not Pareto efficient, then it is Pareto _________ by another alternative.”

  • The digit is the correct answer: What type of marriage are Gale and Shapley aiming for? (1) happy, (2) long, (3) stable, (4) successful, (5) romantic, (6) intermittent, (7) concurrent, (8) eternal.