Comparing three simultaneous measurements of a sociocognitive network

Three data collection strategies are compared in their ability to measure a globally shared cognitive network representation, i.e. a sociocognitive network. Participant performances in data production using each of the three strategies are also assessed. Data were collected from 22 students in a graduate program. Each participant reported k out of 22 “ordinary” ties (Task 1, 0≤k≤22), m out of k “close” ties (Task 2, 0≤m≤k), and “top three” ties (Task 3) for every actor in the network. Results revealed that each of the three tasks were quite similar to each other in measuring the sociocognitive network. The estimated average shared information among the actors about the network’s structure, as revealed by each task, was highest for Task 2 and lowest for Task 1. Individual differences in performance indicate that the amount of shared knowledge as revealed by each task is not consistent across tasks. Overall, three-way data structures are shown to be sufficiently rich in information that any of the tasks are sufficient to capture the main features of a sociocognitive network.     

Strategy-proofness and the reluctance to make large lies: the case of weak orders

This article incorporates agents’ reluctance to make a large lie into an analysis. A social choice rule is D(k)-proof if the rule is nonmanipulable by false preferences within k distance from the sincere one, where k is a positive integer. If D(k)-proofness is not logically equivalent to strategy-proofness, then agents’ reluctance to make a large lie embodied in D(k)-proofness is effective to construct a nonmanipulable rule. This article considers weak orders as agents’ preferences. I prove that on the universal domain, D(k)-proofness is equivalent to strategy-proofness if and only if k ≥ m ? 1, where m is the number of alternatives. Moreover, I find a sufficient condition on a domain for the equivalence of D(1)-proofness and strategy-proofness.     

Are social equivalences ever regular?: Permutation and exact tests

A regular equivalence on a relation induces matrix blocks that are either 0-blocks or regular-blocks, where a regular-block contains at least one positive entry in each row and column. The authors devise both a permutation test and an exact statistical test that separates these two aspects of regular equivalence, 0-blocks and regular-blocks. To test for the regular-block property, the natural test statistic is the number of rows and columns within each purported regular-block that fail to meet the criteria of having at least one positive entry. This statistic is computed for permutations that fix each regular-block as a whole (alternatively, within each sub-row), except for diagonal blocks, for which the diagonal entries are individually fixed. The exact test is derived by assuming that the number of zeros in each block is fixed and that each permutation of zeros is uniformly distributed. This implies that the probability of finding, say, k zeros in a given set of rows and columns follows the hypergeometric distribution, known in physics as the Fermi–Dirac statistics. These results from the separate blocks are combined by convolution to give the distribution of k zero vectors in the matrix as a whole. These tests were applied to data sets from Sampson’s Monastery, Wasserman and Faust’s Countries Trade Networks, Krackhardt’s High-Tech Managers, and B.J. Cole’s Dominance Hierarchies in Leptothorax ants. In all four cases, the 0-blocks were very significant, having only a tiny fraction of permutations with fewer errors than was found in the data. With the regular-blocks, however, there was no significant relation in the Countries data and a significant overall tendency in the other three data sets toward having more departures from regular 1-blocks in the data than in the permuted matrices.     

Individual powers and social consent: an axiomatic approach

We introduce a notion of conditionally decisive powers the exercise of which depends on social consent. Decisive powers, or the so-called libertarian rights, are examples and much weaker forms of powers are covered by our notion. We provide an axiomatic characterization of existence of a system of powers and its uniqueness as well as characterizations of various families of rules represented by systems of powers. Critical axioms are monotonicity, independence and symmetric linkage (person i and i’s issues should be treated symmetrically to person j and j’s issues for at least one linkage between issues and persons).     

The core of social choice problems with monotone preferences and a feasibility constraint

We consider collective choice with agents possessing strictly monotone, strictly convex and continuous preferences over a compact and convex constraint set contained in ₊^k . If it is non-empty the core will lie on the efficient boundary of the constraint set and any policy not in the core is beaten by some policy on the efficient boundary. It is possible to translate the collective choice problem on this efficient boundary to another social choice problem on a compact and convex subset of ₊^c (c<k) with strictly convex and continuous preferences. In this setting the dimensionality results in Banks (1995) and Saari (1997) apply to the dimensionality of the boundary of the constraint set (which is lower than the dimensionality of the choice space by at least one). If the constraint set is not convex then the translated lower dimensional problem does not necessarily involve strict convexity of preferences but the dimensionality of the problem is still lower. Broadly, the results show that the homogeneity afforded by strict monotonicity of preferences and a compact constraint set makes generic core emptyness slightly less common. One example of the results is that if preferences are strictly monotone and convex on ² then choice on a compact and convex constraint exhibits a version of the median voter theorem.I thank Donald Saari for helpful comments on an earlier version of this paper.     

Actions of symmetry groups

This paper studies maps which are invariant under the action of the symmetry group S _k . The problem originates in social choice theory: there are k individuals each with a space of preferences X, and a social choice map :X ^k X which is anonymous i.e. invariant under the action of a group of symmetries. Theorem 1 proves that a full range map :X ^k X exists which is invariant under the action of S _k only if, for all i1, the elements of the homotopy group _i (X) have orders relatively prime with k. Theorem 2 derives a similar results for actions of subgroups of the group S _k . Theorem 3 proves necessary and sufficient condition for a parafinite CW complex X to admit full range invariant maps for any prime number k:X must be contractible.Hospitality and research support from the Standard Institute for Theoretical Economics during the summer of 1991 is gratefully acknowledged. This paper was presented at a Colloquium in the Department of Mathematics, Columbia University, February 6, 1991. I thank the participants of the Colloquium and Jerry Kelly for helpful comments.     

A study of sign adjustment in weighted signed networks

We analyse the adjustment of networks comprising of weighted positive (P) and negative (N) symmetric relations under the impact of various balancing rules. Five kinds of rules are studied: (1) a local minimal edge adjustment which is a special case of, (2) a local pressure based rule, (3) a local sign based rule, (4) a global rule and (5) rules varying on a local to global dimension. The convergence and convergent proportions of different 3-cycles and, thus the impact upon β(3) balance, under the different kinds of adjustment rule are studied both analytically and through simulation. The effects of network size (n), density (d) and the initial proportion of positive edges (α₀) upon the convergence of 3-cycles and, thus, balance and the eventual implications for the process of group formation are explored.     

On the characterization of liberalism by Samet and Schmeidler

In the model of group identification, Samet and Schmeidler (J Econ Theory 110:213–233, 2003) provide two axiomatic characterizations of the“liberal” decision rule (a person is socially qualified as a member of a collective if and only if he qualifies himself). They impose standard monotonicity, non-degeneracy, and independence axioms, together with either exclusive self-determination (opinions by disqualified persons about qualified persons should not matter) or affirmative self-determination (social decision on who are qualified should coincide with social decision on who should be the qualifiers). Dropping monotonicity (and also non-degeneracy in a result) and considering a more general domain to allow neutral opinions, we characterize a larger family of “self-dependent” rules that share the important feature of liberalism that qualification of i depends only on i’s own opinion about himself or herself. Samet and Schmeidler’s results can be obtained with a weaker set of axioms and with a more general domain condition.     

A general concept of procedural fairness for one-stage implementation

A requirement of procedural fairness is introduced and imposed on game forms. According to this axiom, everybody should be able, by varying unilaterally one`s strategy while keeping the others' strategies fixed, to produce the same set of outcomes. This axiom is called « Equality of Attainable Sets ». A necessary and sufficient condition for Nash implementability with Equality of Attainable Sets is provided under a mild domain restriction. This condition is shown to be equivalent to Nash implementability in structured models where each agent is homo oeconomicus.I thank C. d'Aspremont, S. Barbera, K. Binmore, J. Roemer, L. Gevers and an anonymous referee for their comments. The usual disclaimer applies.     

Top-Pair and Top-Triple Monotonicity

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.     

k-means-based algorithm for blockmodeling linked networks

The paper presents a k-means-based algorithm for blockmodeling linked networks where linked networks are defined as a collection of one-mode and two-mode networks in which units from different one-mode networks are connected through two-mode networks. The reason for this is that a faster algorithm is needed for blockmodeling linked networks that can better scale to larger networks. Examples of linked networks include multilevel networks, dynamic networks, dynamic multilevel networks, and meta-networks. Generalized blockmodeling has been developed for linked/multilevel networks, yet the generalized blockmodeling approach is too slow for analyzing larger networks. Therefore, the flexibility of generalized blockmodeling is sacrificed for the speed of k-means-based approaches, thus allowing the analysis of larger networks. The presented algorithm is based on the two-mode k-means (or KL-means) algorithm for two-mode networks or matrices. As a side product, an algorithm for one-mode blockmodeling of one-mode networks is presented. The algorithm’s use on a dynamic multilevel network with more than 400 units is presented. A situation study is also conducted which shows that k-means based algorithms are superior to relocation algorithm-based methods for larger networks (e.g. larger than 800 units) and never much worse.     

On the manipulability of approval voting and related scoring rules

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of candidates: by comparison of worst candidates, best candidates, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of candidates. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable—has the smallest number of manipulable preference profiles—under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the k-approval rule with k around half the number of candidates is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned.     

Extending the Condorcet Jury Theorem to a general dependent jury

We investigate necessary and sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem (CJT). In the Bayesian game G _n among n jurors, we allow for arbitrary distribution on the types of jurors. In particular, any kind of dependency is possible. If each juror i has a ??constant strategy??, ?? ⁱ (that is, a strategy that is independent of the size n ?? i of the jury), such that ?? = (?? ¹, ?? ², . . . , ?? ⁿ . . .) satisfies the CJT, then by McLennan (Am Political Sci Rev 92:413?C419, 1998) there exists a Bayesian-Nash equilibrium that also satisfies the CJT. We translate the CJT condition on sequences of constant strategies into the following problem:

(**) For a given sequence of binary random variables X?=?(X ¹, X ², . . . , X ⁿ , . . .) with joint distribution P, does the distribution P satisfy the asymptotic part of the CJT?

We provide sufficient conditions and two general (distinct) necessary conditions for (**). We give a complete solution to this problem when X is a sequence of exchangeable binary random variables.     

A theory of policy differentiation in single issue electoral politics

Voter preferences are characterized by a parameter s (say, income) distributed on a set S according to a probability measure F. There is a single issue (say, a tax rate) whose level, b, is to be politically decided. There are two parties, each of which is a perfect agent of some constituency of voters, voters with a given value of s. An equilibrium of the electoral game is a pair of policies, b ₁ and b ₂, proposed by the two parties, such that b _i maximizes the expected utility of the voters whom party i represents, given the policy proposed by the opposition. Under reasonable assumptions, the unique electoral equilibrium consists in both parties proposing the favorite policy of the median voter. What theory can explain why, historically, we observe electoral equilibria where the ‘right’ and ‘left’ parties propose different policies? Uncertainty concerning the distribution of voters is introduced. Let {F(t)} _{t ε T} be a class of probability measures on S; all voters and parties share a common prior that the distribution of t is described by a probability measure H on T. If H has finite support, there is in general no electoral equilibrium. However, if H is continuous, then electoral equilibrium generally exists, and in equilibrium the parties propose different policies. Convergence of equilibrium to median voter politics is proved as uncertainty about the distribution of voter traits becomes small.     

The value of a player in n-person games

. The article decomposes the Shapley value into a value matrix which gives the value of every player to every other player in n-person games. Element Φ_ij(v) in the value matrix is positive, zero, or negative, dependent on whether row player i is beneficial, has no impact, or is not beneficial for column player j. The elements in each row and in each column of the value matrix sum up to the Shapley value of the respective player. The value matrix is illustrated by the voting procedure in the European Council of Ministers 1981–1995. Received: 9 September 1998/Accepted: 11 February 2000     

Pollen specialization by solitary bees in an urban landscape

Many polylectic bee species are known to specialize locally on one or a few pollen types to increase foraging efficiency. What is relatively unknown is how different landscapes influence foraging decisions, and whether habitat alteration, such as that resulting from urbanization, influences broad-scale foraging activities of bees. This study evaluates the type and diversity of pollen collected by two solitary bees that are common in Toronto, Ontario, Canada, the native Osmia pumila and the exotic O. caerulescens, sampled in trap nests set up in urban parks and gardens. We found that the dominant pollen in every successful brood cell was either of one widespread, cosmopolitan lawn-invasive plant species (Trifolium repens) or one of two wind-pollinated tree genera (Quercus spp. and Betula spp.). In combination, these three represented more than 90 % of all pollen collected by each bee species. Despite considerable overlap in the dominant pollen types collected by each bee species, the exotic O. caerulescens was significantly more specialized than the native O. pumila. Brood cells with Betula as the dominant pollen type were more pollen species-rich than those cells having Trifolium or Quercus as dominant, perhaps a result of the comparatively low protein content in Betula pollen.     

Defectors’ niches: prisoner's dilemma game on disordered networks

Effects of disordered networks on evolution of cooperation are studied based on the prisoner's dilemma game on a random regular relational graph. As a parameter q (0 ≤ q ≤ 1) that controls a degree of randomness of the network varies from zero to unity, the initial two-dimensional square lattice network becomes more relationally randomized while regularity of the network is kept. It is shown that random connections that make possible cooperator jump into defectors’ clusters ironically trigger the formation of defectors’ niches, in which defectors impose upon cooperators and do not have incentive to change their strategy.     

A new method for finding hierarchical subgroups from networks

We present a new method for decomposing a social network into an optimal number of hierarchical subgroups. With a perfect hierarchical subgroup defined as one in which every member is automorphically equivalent to each other, the method uses the REGGE algorithm to measure the similarities among nodes and applies the k-means method to group the nodes that have congruent profiles of dissimilarities with other nodes into various numbers of hierarchical subgroups. The best number of subgroups is determined by minimizing the intra-cluster variance of dissimilarity subject to the constraint that the improvement in going to more subgroups is better than a network whose n nodes are maximally dispersed in the n-dimensional space would achieve. We also describe a decomposability metric that assesses the deviation of a real network from the ideal one that contains only perfect hierarchical subgroups. Four well known network data sets are used to demonstrate the method and metric. These demonstrations indicate the utility of our approach and suggest how it can be used in a complementary way to Generalized Blockmodeling for hierarchical decomposition.     

The Rise of Rational Choice Theory as a Scientific/Intellectual Movement in Sociology

How did Rational Choice Theory (RCT), traditionally rejected by sociologists for its economic individualism, rise rapidly in the 1980s and the 1990s to theoretical and institutional prominence within sociology? Drawing on Frickel and Gross’ (American Sociological Association, 70(2):204–232 2005) framework for the emergence of scientific/intellectual movements (SIMs), we argue that RCT rose to prominence in sociology in conjunction with: 1) high status actors’ criticism of the previously dominant paradigm, structural functionalism; 2) favorable structural conditions that provided entrepreneurial access to key resources; 3) proliferation through micromobilization contexts; and 4) the ability of those espousing RCT for sociology to draw on dominant cultural motifs outside of academia. The rise of RCT in American sociology provides a case study for how scientific/intellectual movements can find an audience in academic contexts that are predisposed to oppose them.     

Factors determining the occupancy of Trumpeter Hornbills in urban-forest mosaics of KwaZulu-Natal,South Africa

Understanding the factors determining the occupancy and detection probability of birds in human dominated environments is important for their conservation. In this study we investigated various environmental variables believed to influence the site occupancy and detection probability of Trumpeter Hornbill (Bycanistes bucinator) in urban-forest mosaics of KwaZulu-Natal, South Africa. Presence/absence data were collected from a total of 50 point count stations established between September 2014 and March 2015 in urban-forest mosaics of Durban, Eshowe and Mtunzini. Mean occupancy rate of Trumpeter Hornbill was 0.40 ± 0.09 with a low detection probability of 0.28 ± 0.04. For Trumpeter Hornbills, large trees influenced their occupancy positively (sum AIC weight (ω _i ) = 79%) while relative human abundance negatively influenced their occupancy (ω _i = 91%). Model selection suggested that housing density had a strong negative influence on detection probability of Trumpeter Hornbills (ω _i ?=?82?%?) and availability of fruiting trees influenced their detection positively (ω _i ?=?29%). With continued changing land use in KwaZulu-Natal, these finding are important for conservation of Trumpeter Hornbills as we provide insight into landscape variables or features that influence Trumpeter Hornbill’s occupancy and detection in areas of urban-forest mosaics.