Classification theorem for smooth social choice on a manifold

A classification theorem for voting rules on a smooth choice space W of dimension w is presented. It is shown that, for any non-collegial voting rule, σ, there exist integers v ^*(σ), w ^*(σ) (with v ^*(σ)<w ^*(σ)) such that

1. structurally stable σ-voting cycles may always be constructed when w ? v ^*(σ) + 1
2. a structurally stable σ-core (or voting equilibrium) may be constructed when w ? v ^*(σ) ? 1

Finally, it is shown that for an anonymous q-rule, a structurally stable core exists in dimension \(\frac{{n - 2}}{{n - q}}\) , where n is the cardinality of the society.     

Subgroup independence conditions on preferences

The concept of n-scale independence is introduced for a preference relation defined on ${\mathbb{R}^{n}=\mathbb{R}^{n_{1}}\times \cdots \times \mathbb{R}^{n_{p}}}$ . In addition to zero-independence and upper semicontinuity at zero, n-scale independence allows us to characterizate linear oligarchies as well as to offer a (semi)continuous welfarist analogue of Wilson’s theorem. We also include a characterization of the class of continuous, n-separable and n-scale independent, p ≥ 3, social orderings in terms of what we call homogeneous oligarchies.     

Collective labor supply with many consumption goods

We extend Chiappori??s (J Polit Econ 100:437?C467, 1992) standard, ??collective?? model of labor supply to the case of several consumption goods. We show that more robust estimates obtain. Moreover, individual demands for each commodity, although unobservable, can be recovered up to an additive constant. In particular, the impact of changes in wages, non labor income or distribution factors on individual consumption patterns can be identified even though no individual consumption is observed.     

The inverse Banzhaf problem

Let ${\mathcal{F}}Let F{\mathcal{F}} be a family of subsets of the ground set [n] = {1, 2, . . . , n}. For each i ? [n]{i \in [n]} we let p(F,i){p(\mathcal{F},i)} be the number of pairs of subsets that differ in the element i and exactly one of them is in F{\mathcal{F}}. We interpret p(F,i){p(\mathcal{F},i)} as the influence of that element. The normalized Banzhaf vector of F{\mathcal{F}}, denoted B(F){B(\mathcal{F})}, is the vector (B(F,1),...,B(F,n)){(B(\mathcal{F},1),\dots,B(\mathcal{F},n))}, where B(F,i)=\fracp(F,i)p(F){B(\mathcal{F},i)=\frac{p(\mathcal{F},i)}{p(\mathcal{F})}} and p(F){p(\mathcal{F})} is the sum of all p(F,i){p(\mathcal{F},i)}. The Banzhaf vector has been studied in the context of measuring voting power in voting games as well as in Boolean circuit theory. In this paper we investigate which non-negative vectors of sum 1 can be closely approximated by Banzhaf vectors of simple voting games. In particular, we show that if a vector has most of its weight concentrated in k < n coordinates, then it must be essentially the Banzhaf vector of some simple voting game with n − k dummy voters.     

Boolean analysis of questionnaire data

The principle of Boolean analysis is to look for entailments between variables in a questionnaire. If all the respondents answering “yes” to the question X answers “yes” to the question Y, we note the entailment X → Y. Boolean algebra generalizes this approach. A questionnaire of n binary variables generates a set of 2ⁿ possible patterns of response. These patterns generate a Boolean algebra. If only some of the possible patterns are present, the bipartition in this set defines a Boolean equation, the solutions of which are entailments. Usually we use approximations of this structure to analyse a questionnaire. A presentation of the method is given here with application to sociological data.     

Nest predators,but not nest survival,differ between adjacent urban habitats

Growing human populations make it imperative for ecologists to identify strategies to conserve biodiversity in human-dominated landscapes, such as cities. Effects of urbanization on birds are particularly well-studied, but questions remain regarding the best conservation approaches. Debate about the relative utility of focusing conservation efforts on nature reserves versus developed lands has focused largely on comparing species abundance or presence, with few studies addressing underlying behavioral or demographic mechanisms. Here we evaluated differences in avian reproductive success in nature reserves and matrix habitats to test the assumption that nest predation is lower within areas protected from development. Specifically, we investigated 1) whether nest survival differed in replicated pairs of forest parks and residential neighborhoods and 2) whether differences in nest survival were associated with changes in which species most frequently depredated nests. From April–August 2007–2014, we monitored nests of two native birds, American robin (Turdus migratorius) and northern cardinal (Cardinalis cardinalis), and video-documented nest predators in paired forest-matrix habitats in the Columbus, Ohio metropolitan area. We found similar rates of nest survival in the two habitats for both robins (Χ²₁?=?0.715, p?=?0.398, n?=?741 nests) and cardinals (Χ²₁?=?0.926, p?=?0.336, n?=?1156 nests), but interactions between predators and prey differed. In particular, domestic cats (Felis catus) were over five times as likely to depredate cardinal nests in matrix habitats versus forest parks (Χ²₁?=?7.24, simulated p?=?0.010; n_forest?=?3, n_matrix?=?7). Our results suggest that at least in some circumstances, nest success of native birds may be equivalent between nature reserves and adjacent residential matrix habitats, and thus residential neighborhoods may contribute positively to bird conservation in urban landscapes.     

Balanced allocation methods for claims problems with indivisibilities

We study claims problems in which a certain amount of indivisible units (of an homogeneous good) has to be distributed among a group of agents, when this amount is not enough to fully satisfy agents’ demands. Our aim is to find solutions fulfilling procedural and fairness properties. To do that, we define the M-down methods, which are the unique robust (composition down and consistency) and fair (balancedness and conditional full compensation) rules. Besides, we also establish the relationship between these M-down methods and the constrained equal awards rule.     

Path independent choice and the ranking of opportunity sets

The indirect utility principle provides an instrumentalist basis for ranking opportunity sets, given an underlying preference ranking on alternatives. Opportunity set A is weakly preferred to B if A includes at least one preference-maximising element from $A\cup B$ . We introduce the Plott consistency principle as a natural extension of this logic to decision-makers who choose amongst alternatives according to a path independent choice function. Such choice functions need not be rationalisable by a preference order. Plott consistency requires that A is an acceptable choice from $\left\{ A, B\right\} $ if A includes at least one element from the set of acceptable choices from $A\cup B$ . We explore necessary and sufficient conditions (imposed on a choice function defined on collections of opportunity sets) for Plott consistency.     

Invariance axioms for preferences: applications to social choice theory

I investigate the role played by the combination of two invariance axioms for preferences in utility theory; namely, those of zero-independence and scale-independence, respectively. I provide a characterization of the preference relations on ${\mathbb{R}^{n}}$ that satisfy these two axioms as those which are either trivial, or what I call a two-serial total preorder on ${\mathbb{R}^{n}}$ . This result is then applied in social choice theory to characterize those social welfare functions that satisfy IIA and PI. Other characterizations involving the usual Pareto concepts are also provided.     

Implementation of Jefferson-d’Hondt rule in the formation of a parliamentary committee

Same parliaments, to form a committee of size $q$ , use a voting process like the following: every parliamentary member votes for one out of a fixed set of candidates, and those $q$ candidates receiving more votes are elected for the committee. Assuming total discipline of vote, this is a game form in which players are the parliamentary groups. We investigate, according to some natural hypotheses about preferences, the likely distribution of the members of this committee. The main results are: (a) when fractional votes are allowed, there is a complete agreement between the distribution among the groups of the elected candidates that are outcomes of a Nash equilibrium and the distribution that, according to the size of the groups, would compute the Jefferson-d’Hondt allocation rule, and (b) when fractional votes are not allowed, there is a near agreement for a majority of situations.     

How the size of a coalition affects its chances to influence an election

Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of k voters to all voting situations is no greater than $D_{m} \frac{k}{n}Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of k voters to all voting situations is no greater than , where D _m is a constant which depends only on the number m of alternatives but not on k and n. Recent results on individual manipulability in three alternative elections show that this estimate is exact for k=1 and m=3.

Arkadii SlinkoEmail:

     

Uniform trade rules for uncleared markets

We analyze markets in which the price of a traded commodity is such that the supply and the demand are unequal. Under standard assumptions, the agents then have single peaked preferences on their consumption or production choices. For such markets, we propose a class of Uniform trade rules each of which determines the volume of trade as the median of total demand, total supply, and an exogenous constant. Then these rules allocate this volume “uniformly” on either side of the market. We evaluate these “trade rules” on the basis of some standard axioms in the literature. We show that they uniquely satisfy Pareto optimality, strategy proofness, no-envy, and an informational simplicity axiom that we introduce. We also analyze the implications of anonymity, renegotiation proofness, and voluntary trade on this domain.     

Sticky floors and glass ceilings in Latin America

We employ unconditional quantile-decomposition methods to analyze the gender wage gap (gwg) in the urban region of twelve Latin American countries. Using data from harmonized household surveys we decompose the gwg into an explained component (differences in human capital) and an unexplained component (different rates of return to human capital). We find evidence of sticky floors (larger gwg at the tenth percentile than at the median) and glass ceilings (larger gwg at the ninetieth percentile than at the median). The former are more frequent and their magnitude is generally larger. Working women are more educated than working men all along the wage distribution, which partially hides the ‘unexplained’ pay difference. Finally, we find that poorer countries and countries with more income inequality have higher gwg at the tenth percentile of the wage distribution. Richer countries and countries with lower inequality present larger gwg at the ninetieth percent of the wage distribution.     

Accuracy of Inferring Self- and Other-Preferences from Spontaneous Facial Expressions

Participants?? faces were covertly recorded while they rated the attractiveness of people, the decorative appeal of paintings, and the cuteness of animals. Ratings employed a continuous scale. The same participants then returned and tried to guess ratings from 3-s videotapes of themselves and other targets. Performance was above chance in all three stimulus categories, thereby replicating the results of an earlier study (North et al. in J Exp Soc Psychol 46(6):1109?C1113, 2010) but this time using a more sensitive rating procedure. Across conditions, accuracy in reading one??s own face was not reliably better than other-accuracy. We discuss our findings in the context of ??simulation?? theories of face-based emotion recognition (Goldman in The philosophy, psychology, and neuroscience of mindreading. Oxford University Press, Oxford, 2006) and the larger body of accuracy research.     

The original Borda count and partial voting

In a Borda count, bc, M. de Borda suggested the last preference cast should receive 1 point, the voter’s penultimate ranking should get 2 points, and so on. Today, however, points are often awarded to (first, second,..., last) preferences cast as per (n, n?1, ..., 1) or more frequently, (n ?1, n?2,..., 0). If partial voting is allowed, and if a first preference is to be given n or n ? 1 points regardless of how many preferences the voter casts, he/she will be incentivised to rank only one option/candidate. If everyone acts in this way, the bc metamorphoses into a plurality vote... which de Borda criticized at length. If all the voters submit full ballots, the outcome—social choice or ranking—will be the same under any of the above three counting procedures. In the event of one or more persons submitting a partial vote, however, outcomes may vary considerably. This preliminary paper suggests research should consider partial voting. The author examines the consequences of the various rules so far advocated and then purports that M. de Borda, in using his formula, was perhaps more astute than the science has hitherto recognised.     

Influence of urbanization on the occurrence and activity of aerial insectivorous bats

Activity and species-specific responses of insectivorous bats in different urban-forest conditions provides a general perspective on the adaptability and vulnerability of bat species towards urbanization intensity. Here we evaluated species richness and activity patterns of aerial insectivorous bats across an urbanized landscape in the highlands of Chiapas, in Mexico. Acoustic monitoring of echolocation calls was conducted for 27 nights over a period of four months. Species richness and relative activity of insectivorous bats were estimated in a landscape with different conditions of urbanization intensity: urban areas, non-urban and forest areas. We identified a total of 14 bat species and three phonotypes. Bat species richness and relative activity was similar (X² = 0.568, gl = 2, p > 0.05), but species composition differed among conditions. We observed a significant higher occurrence of Bauerus dubiaquercus, Eptesicus brasiliensis and Myotis californicus in forest sites. Urban sites presented higher occurrence of Molossus rufus and phonotype Molossidae 2, while non-urban sites presented a higher occurrence of Eptesicus furinalis and phonotype Molossidae 2. We were able to identify bat species according to their relative activity in relation todifferent landscape conditions. Species of the Molossidae family presented the highest activity in urban sites, which was positively affected by the number of streetlights, while species of the Vespertilionidae presented the highest activity in forest sites, which was positively related totree density. While urbanization tends to diminish native biodiversity and alter faunal communities, our results show a similar richness and relative activity of aerial insectivorous bats along the urban ecosystem. The effect of urbanization intensity becomes more apparent in species-specific bat activity; the response of species towards particular habitat conditions depends on local habitat quality and characteristics (i.e., presence of streetlights, vegetation cover and tree density).     

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.     

The ��Semiotic Self��: From Peirce and Mead to Wiley and Singer

Norbert Wiley (1994) provides a synthesis of Peirce??s and Mead??s views on the self. The Peirce-Mead ideal type model of the self involves the I and the me as well as the I and the you. Hence, at each moment we are a combined ??me-I-you?? in past, present and future. Milton Singer (1989) discovers the semiotic self through his anthropological research, but does not apply the concept as rigorously as one might hope. Peirce??s triadic epistemology and Pragmatism is explored to frame his contribution to the semiotic self. His categories of Firstness, Secondnes and Thirdness are briefly considered. Some anecdotal information about the self in Indic Civilization is discussed. It is argued that the INSOR model can be useful. The key is to move beyond Cartesian notions and to see the semotic self as a ??semiotic object,?? always subject to interpretation by the person engaged in symbolic interaction and exchange.     

Choice in ordered-tree-based decision problems

Decision makers often have to choose alternatives which appear in an exogenous structure. For example, consider choosing a dish in a restaurant after going through different menu cards (a menu card for buffet, another for combo offers etc.). The decision maker observes the items displayed (as a list) on a menu card and she switches to another menu card to see the items displayed on it (again in the form of another list). Thus the set of all items appears as an “ordered-tree” to the decision maker. There are other examples of decision making where alternatives appear in the form of an ordered-tree. In this paper we consider the cases of choice from ordered-trees (in particular, “lists of lists”) and characterize the choice functions. We impose the axioms of Backward Consistency and Replacement Indifference on choice functions and obtain characterization results for \(k\) -ary ordered-trees and more general ordered-trees. We show that the results for \(k=2\) are similar to those of (Rubinstein and Salant 2006), in which the cases of choice from lists are considered. However the results for \(k \ge 3\) and general ordered-trees are different and allow for instance, a richer class of tie-breaking rules in special cases.     

On the equivalence between progressive taxation and inequality reduction

We establish the precise connections between progressive taxation and inequality reduction, in a setting where the level of tax revenue to be raised is exogenously fixed and tax schemes are balanced. We show that, in contrast with the traditional literature on taxation, the equivalence between inequality reduction and the combination of progressivity and income order preservation does not always hold in this setting. However, we show that, among rules satisfying consistency and, either revenue continuity, or revenue monotonicity, the equivalence remains intact.