arXiv subjects

Kimmo Eriksson

Publications and source records attributed to Kimmo Eriksson.

15 recordsLinked to original sources

arXiv2025

AI Models Exceed Individual Human Accuracy in Predicting Everyday Social Norms

A fundamental question in cognitive science concerns how social norms are acquired and represented. While humans typically learn norms through embodied social experience, we investigated whether large language models can achieve sophisticated norm understanding through statistical learning alone. Across two studies, we systematically evaluated multiple AI systems' ability to predict human social appropriateness judgments for 555 everyday scenarios by examining how closely they predicted the average judgment compared to each human participant. In Study 1, GPT-4.5's accuracy in predicting the collective judgment on a continuous scale exceeded that of every human participant (100th percentile). Study 2 replicated this, with Gemini 2.5 Pro outperforming 98.7% of humans, GPT-5 97.8%, and Claude Sonnet 4 96.0%. Despite this predictive power, all models showed systematic, correlated errors. These findings demonstrate that sophisticated models of social cognition can emerge from statistical learning over linguistic data alone, challenging strong versions of theories emphasizing the exclusive necessity of embodied experience for cultural competence. The systematic nature of AI limitations across different architectures indicates potential boundaries of pattern-based social understanding, while the models' ability to outperform nearly all individual humans in this predictive task suggests that language serves as a remarkably rich repository for cultural knowledge transmission.

cs.AI↗

arXiv2025

What Makes AI Applications Acceptable or Unacceptable? A Predictive Moral Framework

As artificial intelligence rapidly transforms society, developers and policymakers struggle to anticipate which applications will face public moral resistance. We propose that these judgments are not idiosyncratic but systematic and predictable. In a large, preregistered study (N = 587, U.S. representative sample), we used a comprehensive taxonomy of 100 AI applications spanning personal and organizational contexts-including both functional uses and the moral treatment of AI itself. In participants' collective judgment, applications ranged from highly unacceptable to fully acceptable. We found this variation was strongly predictable: five core moral qualities-perceived risk, benefit, dishonesty, unnaturalness, and reduced accountability-collectively explained over 90% of the variance in acceptability ratings. The framework demonstrated strong predictive power across all domains and successfully predicted individual-level judgments for held-out applications. These findings reveal that a structured moral psychology underlies public evaluation of new technologies, offering a powerful tool for anticipating public resistance and guiding responsible innovation in AI.

cs.CY↗

arXiv2017

Limit shapes of stable configurations of a generalized Bulgarian solitaire

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, $σ$-Bulgarian solitaire, the number of cards you pick from a pile is some function $σ$ of the pile size, such that you pick $σ(h)\le h$ cards from a pile of size $h$. Here we consider a special class of such functions. Let us call $σ$ well-behaved if $σ(1)=1$ and if both $σ(h)$ and $h-σ(h)$ are non-decreasing functions of $h$. Well-behaved $σ$-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 ($λ_1 \ge λ_2\ge \dots$) then a configuration is convex if and only if it is a stable configuration of some well-behaved $σ$-Bulgarian solitaire. If sorted configurations are represented by Young diagrams and scaled down to have unit height and unit area, the stable configurations corresponding to an infinite sequence of well-behaved functions ($σ_1, σ_2, \dots$) may tend to a limit shape $ϕ$. We show that every convex $ϕ$ with certain properties can arise as the limit shape of some sequence of well-behaved $σ_n$. For the special case when $σ_n(h)=\lceil q_n h \rceil$ for $0 < q_n \le 1$, these limit shapes are triangular (in case $q_n^2 n\rightarrow 0$), or exponential (in case $q_n^2 n\rightarrow \infty$), or interpolating between these shapes (in case $q_n^2 n\rightarrow C>0$).

math.CO↗

arXiv2017

An exponential limit shape of random $q$-proportion Bulgarian solitaire

We introduce \emph{$p_n$-random $q_n$-proportion Bulgarian solitaire} ($0<p_n,q_n\le 1$), played on $n$ cards distributed in piles. In each pile, a number of cards equal to the proportion $q_n$ of the pile size rounded upward to the nearest integer are candidates to be picked. Each candidate card is picked with probability $p_n$, independently of other candidate cards. This generalizes Popov's random Bulgarian solitaire, in which there is a single candidate card in each pile. Popov showed that a triangular limit shape is obtained for a fixed $p$ as $n$ tends to infinity. Here we let both $p_n$ and $q_n$ vary with $n$. We show that under the conditions $q_n^2 p_n n/{\log n}\rightarrow \infty$ and $p_n q_n \rightarrow 0$ as $n\to\infty$, the $p_n$-random $q_n$-proportion Bulgarian solitaire has an exponential limit shape.

math.PR↗

arXiv2015

The Limit Shape of a Stochastic Bulgarian Solitaire

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.

math.PR↗

arXiv2015

Markov chains on graded posets: Compatibility of up-directed and down-directed transition probabilities

We consider two types of discrete-time Markov chains where the state space is a graded poset and the transitions are taken along the covering relations in the poset. The first type of Markov chain goes only in one direction, either up or down in the poset (an \emph{up chain} or \emph{down chain}). The second type toggles between two adjacent rank levels (an \emph{up-and-down chain}). We introduce two compatibility concepts between the up-directed transition probabilities (an \emph{up rule}) and the down-directed (a \emph{down rule}), and we relate these to compatibility between up-and-down chains. This framework is used to prove a conjecture about a limit shape for a process on Young's lattice. Finally, we settle the questions whether the reverse of an up chain is a down chain for some down rule and whether there exists an up or down chain at all if the rank function is not bounded.

math.PR↗

arXiv2013

Conjugacy of Coxeter elements

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.

math.CO↗

arXiv2008

Words with intervening neighbours in infinite Coxeter groups are reduced

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 irreducible if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of irreducible words.

math.CO↗

arXiv2008

The numbers game and Dynkin diagram classification results

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.

math.CO↗

arXiv2004

Expected number of inversions after a sequence of random adjacent transpositions

In the evolution of a genome, the gene sequence is sometimes rearranged, for example by transposition of two adjacent gene blocks. In biocombinatorics, one tries to reconstruct these rearrangement incidents from the resulting permutation. It seems that the algorithms used are too effective and find a shorter path than the real one. For the simplified case of adjacent transpositions, we give expressions for the expected number of inversions after t random moves. This average can be much smaller than t, a fact that has largely been neglected so far.

math.CO↗

arXiv2004

Exact expectations for random graphs and assignments

For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest. For a random bipartite graph we give a formula for the expected time at which a k-assignment appears. This result has bearing upon the random assignment problem.

math.CO↗

arXiv2004

Note on the lamp lighting problem

We answer some questions concerning the so called sigma-game of Sutner. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that every configuration of lamps can be lit if and only if the number of complete matchings in the graph is odd. In the special case of an orthogonal grid one gets a criterion for whether the number of monomer-dimer tilings of an m times n grid is odd or even.

math.CO↗

arXiv2004

Optimal stopping in a two-sided secretary problem

In the "secretary problem", well-known in the theory of optimal stopping, an employer is about to interview a maximum of N secretaries about which she has no prior information. Chow et al. proved that with an optimal strategy the expected rank of the chosen secretary tends to approximately 3.87. We study a two-sided game-theoretic version of this optimal stopping problem, where men search for a woman to marry at the same time as women search for a man to marry. We find that in the unique subgame perfect equilibrium, the expected rank grows as the square root of N and that, surprisingly, the leading coefficient is exactly 1. We also discuss some possible variations.

math.CO↗

arXiv2004

Conjectures on three-dimensional stable matching

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.

math.CO↗

arXiv1998

Stable matching in a common generalization of the marriage and assignment models

In the theory of two-sided matching markets there are two well-known models: the marriage model (where no money is involved) and the assignment model (where payments are involved). Roth and Sotomayor (1990) asked for an explanation for the similarities in behavior between those two models. We address this question by introducing a common generalization that preserves the two important features: the existence of a stable outcome and the lattice property of the set of stable outcomes.

math.CO↗