We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer... more
We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer experiments, we present a couple of conjectures as well as a few counter-examples to other natural but discarded conjectures. In particular, a circular 3D matching is one where women only care about the man, men only care about the dog, and dogs only care about the woman they are matched with. We conjecture that a stable outcome always exists for any circular 3D matching market, and we prove it for markets with at most four agents of each category.
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Prior research using the Moral Foundations Questionnaire (MFQ) has established that political ideology is associated with self-reported reliance on specific moral foundations in moral judgments of acts. MFQ items do not specify the agents... more
Prior research using the Moral Foundations Questionnaire (MFQ) has established that political ideology is associated with self-reported reliance on specific moral foundations in moral judgments of acts. MFQ items do not specify the agents involved in the acts, however. By specifying agents in MFQ items we revealed blatant political double standards. Conservatives thought that the same moral foundation was more relevant if victims were agents that they like (i.e., corporations and other conservatives) but less relevant when the same agents were perpetrators. Liberals showed the same pattern for agents that they like (i.e., news media and other liberals). A UK sample showed much weaker political double standards with respect to corporations and news media, consistent with feelings about corporations and news media being much less politicized in the UK than in the US. We discuss the implications for moral foundations theory.
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Experiments on economic games typically fail to find positive reputational effects of using peer punishment of selfish behavior in social dilemmas. Theorists had expected positive reputational effe ...
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Bulgarian solitaire is played on $n$ cards divided into several piles; a move consists of picking one card from each pile to form a new pile. In a recent generalization, $\sigma$-Bulgarian solitaire, the number of cards you pick from a... more
Bulgarian solitaire is played on $n$ cards divided into several piles; a move consists of picking one card from each pile to form a new pile. In a recent generalization, $\sigma$-Bulgarian solitaire, the number of cards you pick from a pile is some function $\sigma$ of the pile size, such that you pick $\sigma(h)\le h$ cards from a pile of size $h$. Here we consider a special class of such functions. Let us call $\sigma$ well-behaved if $\sigma(1)=1$ and if both $\sigma(h)$ and $h-\sigma(h)$ are non-decreasing functions of $h$. Well-behaved $\sigma$-Bulgarian solitaire has a geometric interpretation in terms of layers at certain levels being picked in each move. It also satisfies that if a stable configuration of $n$ cards exists it is unique. Moreover, if piles are sorted in order of decreasing size ($\lambda_1 \ge \lambda_2\ge \dots$) then a configuration is convex if and only if it is a stable configuration of some well-behaved $\sigma$-Bulgarian solitaire. If sorted configuratio...
In this reply, we reiterate the main point of our 2012 paper, which was that the measure of inequality used by Norton and Ariely (2011) was too difficult for it to yield meaningful results. We describe additional evidence for this... more
In this reply, we reiterate the main point of our 2012 paper, which was that the measure of inequality used by Norton and Ariely (2011) was too difficult for it to yield meaningful results. We describe additional evidence for this conclusion, and we also challenge the conclusion that political differences in perceived and desired inequality are small.
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Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines... more
Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines where most researchers do not master mathematics, the use of mathematics may be held in too much awe. To demonstrate this I conducted an online experiment with 200 participants, all of which had experience of reading research reports and a postgraduate degree (in any subject). Participants were presented with the abstracts from two published papers (one in evolutionary anthropology and one in sociology). Based on these abstracts, participants were asked to judge the quality of the research. Either one or the other of the two abstracts was manipulated through the inclusion of an extra sentence taken from a completely unrelated paper and presenting an equation that made no sense in the context. The abstract that included the meaningless mathematics ten...
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Cooperation in collective action problems and resource dilemmas is often assumed to depend on the values of the individuals involved, such as their degree of unselfishness and tolerance. Societal differences in cooperation and cooperative... more
Cooperation in collective action problems and resource dilemmas is often assumed to depend on the values of the individuals involved, such as their degree of unselfishness and tolerance. Societal differences in cooperation and cooperative norms may therefore result from cultural variation in emphasis on these personal values. Here we draw on several cross-national datasets to examine whether society-level emphasis on unselfishness and tolerance and respect for other people predict how societies vary in cooperation [in a continuous prisoner’s dilemma (PD)] and in norms governing cooperation [in a common pool resource dilemma (CPR)]. The results suggest that high levels of cooperation and cooperative norms are promoted specifically by a cultural emphasis on tolerance.
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Norm enforcement may be important for resolving conflicts and promoting cooperation. However, little is known about how preferred responses to norm violations vary across cultures and across domains. In a preregistered study of 57... more
Norm enforcement may be important for resolving conflicts and promoting cooperation. However, little is known about how preferred responses to norm violations vary across cultures and across domains. In a preregistered study of 57 countries (using convenience samples of 22,863 students and non-students), we measured perceptions of the appropriateness of various responses to a violation of a cooperative norm and to atypical social behaviors. Our findings highlight both cultural universals and cultural variation. We find a universal negative relation between appropriateness ratings of norm violations and appropriateness ratings of responses in the form of confrontation, social ostracism and gossip. Moreover, we find the country variation in the appropriateness of sanctions to be consistent across different norm violations but not across different sanctions. Specifically, in those countries where use of physical confrontation and social ostracism is rated as less appropriate, gossip is...
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Norm enforcement may be important for resolving conflicts and promoting cooperation. However, little is known about how preferred responses to norm violations vary across cultures and across domains. In a preregistered study of 57... more
Norm enforcement may be important for resolving conflicts and promoting cooperation. However, little is known about how preferred responses to norm violations vary across cultures and across domains. In a preregistered study of 57 countries (using convenience samples of 22,863 students and non-students), we measured perceptions of the appropriateness of various responses to a violation of a cooperative norm and to atypical social behaviors. Our findings highlight both cultural universals and cultural variation. We find a universal negative relation between appropriateness ratings of norm violations and appropriateness ratings of responses in the form of confrontation, social ostracism and gossip. Moreover, we find the country variation in the appropriateness of sanctions to be consistent across different norm violations but not across different sanctions. Specifically, in those countries where use of physical confrontation and social ostracism is rated as less appropriate, gossip is...
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One of the many things teachers do is to give feedback on their students’ work. Feedback pointing out mistakes may be a key to learning, but it may also backfire. We hypothesized that feedback based on students’ mistakes may have more... more
One of the many things teachers do is to give feedback on their students’ work. Feedback pointing out mistakes may be a key to learning, but it may also backfire. We hypothesized that feedback based on students’ mistakes may have more positive effects in cultures where teachers have greater authority over students, which we assume to be cultures that are high on power distance and religiosity. To test this hypothesis we analyzed data from 49 countries taking part in the 2015 wave of the TIMSS assessment, in which students in the 4th and 8th grades were asked whether their teachers in mathematics and science told them how to do better when they had made a mistake. For each country we could then estimate the association between the reported use of mistake-based feedback and student achievement. Consistent with our hypothesis, the estimated effect of mistake-based feedback was positive only in certain countries, and these countries tended to be high on power distance and religiosity. These results highlight the importance of cultural values in educational practice.
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ABSTRACTViolators of cooperation norms may be informally punished by their peers. How such norm enforcement is judged by others can be regarded as a meta-norm (i.e., a second-order norm). We examined whether meta-norms about peer... more
ABSTRACTViolators of cooperation norms may be informally punished by their peers. How such norm enforcement is judged by others can be regarded as a meta-norm (i.e., a second-order norm). We examined whether meta-norms about peer punishment vary across cultures by having students in eight countries judge animations in which an agent who over-harvested a common resource was punished either by a single peer or by the entire peer group. Whether the punishment was retributive or restorative varied between two studies, and findings were largely consistent across these two types of punishment. Across all countries, punishment was judged as more appropriate when implemented by the entire peer group than by an individual. Differences between countries were revealed in judgments of punishers vs. non-punishers. Specifically, appraisals of punishers were relatively negative in three Western countries and Japan, and more neutral in Pakistan, UAE, Russia, and China, consistent with the influence...
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Research on cultural transmission among Americans has established a bias for transmitting stories that have disgusting elements (such as exposure to rats and maggots). Conceived of as a cultural evolutionary force, this phenomenon is one... more
Research on cultural transmission among Americans has established a bias for transmitting stories that have disgusting elements (such as exposure to rats and maggots). Conceived of as a cultural evolutionary force, this phenomenon is one type of emotional selection. In a series of online studies with Americans and Indians we investigate whether there are cultural differences in emotional selection, such that the transmission process favours different kinds of content in different countries. The first study found a bias for disgusting content (rats and maggots) among Americans but not among Indians. Four subsequent studies focused on how country interacts with kind of emotional content (disgusting vs. happy surprises and good news) in reactions to transmission of stories or information. Whereas Indian participants, compared to Americans, tended to be less interested in, and excited by, transmission of stories and news involving common disgust-elicitors (like rats), the opposite patte...
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Within theories of animal behavior and cultural evolution, social learning or social transmission is the act when an individual acquires a cultural element such as an idea, a behavior or a tool, by observing (or otherwise learning from)... more
Within theories of animal behavior and cultural evolution, social learning or social transmission is the act when an individual acquires a cultural element such as an idea, a behavior or a tool, by observing (or otherwise learning from) another individual (rather than by their own invention of the element, which in the same terminology is called individual learning). The individual that is observed is often called the cultural parent. If social learners choose cultural parents at random, the frequencies of cultural variants among social learners will not change in any systematic way. Theories of conformist social learning investigate the possibility that the choice of cultural parent may be biased toward the most common cultural variant, in which case cultural evolution will become directed toward cultural homogeneity among social learners. For any specific case, a bias for socially learning the most common variant may arise in several ways – e.g., if the common variant is more attractive in itself, or if it is favored by the current norms, i.e. through mechanisms that could just as well bias the choice toward some other variant than the currently most common one. Theories of conformist social learning make a much stronger claim: that biological evolution has favored an innate psychological bias to prefer cultural parents that exhibit common behaviors. This proposed innate bias is called a conformist bias.
People often justify their moral opinions by referring to larger moral concerns (e. g., “It is unfair if homosexuals are not allowed to marry!” vs. “Letting homosexuals marry is against our traditions!”). Is there a general agreement... more
People often justify their moral opinions by referring to larger moral concerns (e. g., “It is unfair if homosexuals are not allowed to marry!” vs. “Letting homosexuals marry is against our traditions!”). Is there a general agreement about what concerns apply to different moral opinions? We used surveys in the United States and the United Kingdom to measure the perceived applicability of eight concerns (harm, violence, fairness, liberty, authority, ingroup, purity, and governmental overreach) to a wide range of moral opinions. Within countries, argument applicability scores were largely similar whether they were calculated among women or men, among young or old, among liberals or conservatives, or among people with or without higher education. Thus, the applicability of a given moral concern to a specific opinion can be viewed as an objective quality of the opinion, largely independent of the population in which it is measured. Finally, we used similar surveys in Israel and Brazil t...
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The essential set of a permutation was defined by Fulton as the set of southeast corners of the diagram of the permutation. In this paper we determine explicit formulas for the average size of the essential set in the two cases of... more
The essential set of a permutation was defined by Fulton as the set of southeast corners of the diagram of the permutation. In this paper we determine explicit formulas for the average size of the essential set in the two cases of arbitrary permutations in $S_n$ and $321$-avoiding permutations in $S_n$. Vexillary permutations are discussed too. We also prove that the generalized Catalan numbers ${r+k-1\choose n}-{r+k-1\choose n-2}$ count $r\times k$-matrices dotted with $n$ dots that are extendable to $321$-avoiding permutation matrices.
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We present a unified theory for permutation models of all the infinite families of finite and affine Weyl groups, including interpretations of the length function and the weak order. We also give new combinatorial proofs of Bott's... more
We present a unified theory for permutation models of all the infinite families of finite and affine Weyl groups, including interpretations of the length function and the weak order. We also give new combinatorial proofs of Bott's formula (in the refined version of Macdonald) for the Poincaré series of these affine Weyl groups.
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We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the $q$-Eulerian identities of Brenti and some generalizations. In particular, we prove an identity involving the golden ratio, which allows... more
We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the $q$-Eulerian identities of Brenti and some generalizations. In particular, we prove an identity involving the golden ratio, which allows us to compute upper bounds on how high a checker can reach in a classical checker-jumping problem, when the rules are relaxed to allow also diagonal jumps.
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For a Coxeter group $(W,S)$, a permutation of the set $S$ is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two... more
For a Coxeter group $(W,S)$, a permutation of the set $S$ is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Coxeter elements are conjugate if and only if they are rotation equivalent. This was known for some special cases but not for Coxeter groups in general.
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Consider a graph with vertex set $S$. A word in the alphabet $S$ has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group... more
Consider a graph with vertex set $S$. A word in the alphabet $S$ has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements. Speyer recently proved that words with the intervening neighbours property are reduced if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of reduced words.
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We consider a stochastic version of Bulgarian solitaire: A number of cards are distributed in piles; in every round a new pile is formed by cards from the old piles, and each card is picked independently with a fixed probability. This... more
We consider a stochastic version of Bulgarian solitaire: A number of cards are distributed in piles; in every round a new pile is formed by cards from the old piles, and each card is picked independently with a fixed probability. This game corresponds to a multi-square birth-and-death process on Young diagrams of integer partitions. We prove that this process converges in a strong sense to an exponential limit shape as the number of cards tends to infinity. Furthermore, we bound the probability of deviation from the limit shape and relate this to the number of rounds played in the solitaire.
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The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at... more
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. Combinatorial reasoning is used to show that those connected graphs with negative integer amplitudes for which the numbers game meets a certain finiteness requirement are precisely the Dynkin diagrams associated with the finite-dimensional complex simple Lie algebras. This strengthens a result originally due to the second author. A more general result is obtained when certain real number amplitudes are allowed. The resulting graphs are in families, each family corresponding to a finite irreducible Coxeter group. These results are used to demonstrate that the only generalized Cartan matrices for which there exist finite edge-colored ranked posets enjoying a certain structure property are the Cartan matrices for the finite-dimensional complex semisimple Lie algebras. In this setting, classifications of the finite-dimensional Kac--Moody algebras and of the finite Coxeter and Weyl groups are re-derived.
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The numbers game is a one-player game played on a nite simple graph with certain \am- plitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform... more
The numbers game is a one-player game played on a nite simple graph with certain \am- plitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. Combinatorial reasoning is used to show that those connected graphs with negative integer amplitudes for which the numbers game meets a certain niteness requirement are pre- cisely the Dynkin diagrams associated with the nite-dimensional complex simple Lie algebras. This strengthens a result originally due to the second author. A more general result is obtained when certain real number amplitudes are allowed. The resulting graphs are in families, each family corresponding to a nite irreducible Coxeter group. These results are used to demon- strate that the only generalized Cartan matrices for which there exist nite edge-colored ranked posets enjoying a certain structure property are the Cartan matrices for the nite-dimensional complex semisimple Lie algebras. In this setting, classications of the nite-dimensional Kac{ Moody algebras and of the nite Coxeter and Weyl groups are re-derived.
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Considering strings over a finite alphabet [Ascr ], say that a string is w-avoiding if it does not contain w as a substring. It is known that the number aw(n) of w-avoiding strings of length n depends only on the autocorrelation of w as... more
Considering strings over a finite alphabet [Ascr ], say that a string is w-avoiding if it does not contain w as a substring. It is known that the number aw(n) of w-avoiding strings of length n depends only on the autocorrelation of w as defined by Guibas–Odlyzko. We give a simple criterion on the autocorrelations of w and w′ for determining whether aw(n) > aw′(n) for all large enough n.
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Determinants of cooperation include ingroup vs. outgroup membership, and individual traits, such as prosociality and trust. We investigated whether these factors can be overridden by beliefs about people's trust. We manipulated the... more
Determinants of cooperation include ingroup vs. outgroup membership, and individual traits, such as prosociality and trust. We investigated whether these factors can be overridden by beliefs about people's trust. We manipulated the information players received about each other's level of general trust, "high" or "low". These levels were either measured (Experiment 1) or just arbitrarily assigned labels (Experiment 2). Players' choices whether to cooperate or defect in a stag hunt (or an assurance game)-where it is mutually beneficial to cooperate, but costly if the partner should fail to do so-were strongly predicted by what they were told about the other player's trust label, as well as by what they were told that the other player was told about their own label. Our findings demonstrate the importance for cooperation in a risky coordination game of both first- and second-order beliefs about how much people trust each other. This supports the idea...
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ABSTRACT
... October 1997 Kimmo Eriksson, Johan Karlander, and Lars-Erik Ollery ... Eg if the productivity is the product of some individual ability measures of the worker and the em-ployer, where the measures are independent of the assignment,... more
... October 1997 Kimmo Eriksson, Johan Karlander, and Lars-Erik Ollery ... Eg if the productivity is the product of some individual ability measures of the worker and the em-ployer, where the measures are independent of the assignment, the productivity matrix is always hierarchical. ...