Distorted Lorenz curves: models and comparisons

The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve $L$ by a function $h$ , giving rise to a distorted Lorenz curve ${\widetilde{L}}=h\circ L$ . In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge (2001) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve $L$ affect the transformed curve ${\widetilde{L}}$ . Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function.     

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.     

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.     

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.     

A measure of distance between judgment sets

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming’s metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in ${A \cap B}$ jointly imply that the propositions in A?B share the same truth value, then the disagreement between A and B over those propositions in A?B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.     

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.     

A law of large numbers for weighted plurality

Consider an election between $k$ candidates in which each voter votes randomly (but not necessarily independently) for a single candidate, and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for this special candidate than any other candidate). Suppose we have a voting rule that takes all of the votes and produces a single outcome and suppose that each individual voter has little effect on the outcome of the voting rule. If the voting rule is a weighted plurality, then we show that with high probability, the preferred candidate will win the election. Conversely, we show that this statement fails for all other reasonable voting rules. This result is an extension of one by Häggström, Kalai and Mossel, who proved the above in the case $k=2$ .     

Preference,topology and measure

A symmetric difference metric topology on the collection of binary relations on a countably infinite set provides a new setting for the study of properties of preferences and, as an illustration, is used to lend credence and meaning to some simple intuitions about properties of binary relations. A finite measure on a \(\sigma \) -algebra over the same collection of binary relations is used to provide support for the topological results.     

Moral hazard and stability

Economists perceive moral hazard as an undesirable problem because it undermines efficiency. Carefully designed contracts can mitigate the moral hazard problem, but this assumes that a team is already formed. This paper demonstrates that these contracts are sometimes the reason why teams do not form. Formally, we study the team formation problem in which the agents’ efforts are not verifiable and the size of teams does not exceed quota \(r\) . We show that if the team members cannot make transfers, then moral hazard affects stability positively in a large class of games. For example, a stable team structure exists if teams produce public goods or if the quota is two. However, these existence results no longer hold if efforts are verifiable.     

Dynamic contests with resource constraints

We study a dynamic contest between two players who compete against each other in $n$ different stages. The players have winning values for each stage of the contest that may vary across the stages as well as heterogeneous resource budgets that decrease from a given stage to the next proportionally to the resources allocated in that stage. We characterize a subgame perfect equilibrium of this dynamic contest and show that when the winning value is equal between the stages, the players’ resource allocations are weakly decreasing over the stages. We also study the effect of several distributions of winning values on the players’ resource allocations. We show both the distribution of winning values that balances the players’ resource allocations and the distribution of winning values that maximizes the players’ total resource allocations.     

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.     

Strategy-proof rules for two public goods: double median rules

We consider the problem of selecting the locations of two (identical) public goods on an interval. Each agent has preferences over pairs of locations, which are induced from single-peaked rankings over single locations: each agent compares pairs of locations by comparing the location he ranks higher in each pair. We introduce a class of “double median rules” and characterize it by means of continuity, anonymity, strategy-proofness, and users only. To each pair of parameter sets, each set in the pair consisting of $(n+1)$ parameters, is associated a rule in the class. It is the rule that selects, for each preference profile, the medians of the peaks and the parameters belonging to each set in the pair. We identify the subclasses of the double median rules satisfying group strategy-proofness, weak efficiency, and double unanimity (or efficiency), respectively. We also discuss the classes of “multiple median rules” and “non-anonymous double median rules”.     

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:

     

Propositionwise judgment aggregation: the general case

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or extended unanimity preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between, 2002), Nehring (Oligarchies in judgment aggregation: a characterization, 2006), Dietrich and List (Soc Choice Welf 29(1):19–33, 2007a) and Dokow and Holzman (J Econ Theory 145(2):495–511, 2010a).     

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.     

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.     

Visitors to Northern Australia: Debating the History of Indigenous Gambling

Was gambling introduced to Indigenous Australians1 1. The author is aware of deliberations around titles used to describe Aboriginal and Torres Strait Islander Australians. Alternative terms such as Indigenous, Aboriginal, Koori and Murri are in common use. For consistency, the term Indigenous Australians (ATSIC, 2002 ATSIC (Aboriginal and Torres Strait Islander Islander Commission). 2002. Review of Electoral Systems. Canberra, ATSIC. [Google Scholar]; Mansell, 2003 Mansell, M. 2003. “Citizenship, assimilation and a treaty”. In Treaty, Edited by: McGlade, H. 5–17. Canberra: Aboriginal Studies Press.  [Google Scholar]) has been used to include all Aboriginal and Torres Strait peoples. by British colonists in 1788 or was it introduced by Macassan fishermen much earlier? Using a variety of literature resources, it is argued that Indigenous Australian gambling did exist in regions along Australia's northern coastlines in pre-colonial times due to the influence of Macassan fishermen. Using an anthropological model, the adoption of card games and gambling is seen as an adaptive response to changes in the lives of Indigenous Australians. It is also argued that Binde's (2005) four conditions for predicting the presence of gambling in traditional societies are not reliable indicators for predicting gambling by Indigenous Australians in northern Australia in pre-colonial times.     

The Sexual Consent Scale–Revised: Development,Reliability, and Preliminary Validity

The Sexual Consent Scale–Revised (SCS–R) measures an individual's beliefs, attitudes, and behaviors with respect to how sexual consent should be and is negotiated between sexual partners. This study extends previous research on sexual consent by revising a scale using the Theory of Planned Behavior (Ajzen, 1991 Ajzen , I. ( 1991 ). The Theory of Planned Behavior . Organizational Behavior and Human Decision Processes , 50 , 179 – 211 .[Crossref], [Web of Science ®] , [Google Scholar], 2001 Ajzen , I. ( 2001 ). Attitudes . Annual Review of Psychology , 52 , 27 – 58 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 2005 Ajzen , I. ( 2005 ) . Attitudes, personality, and behavior ( , 2nd ed. ). Milton-Keynes , England : Open University Press/McGraw-Hill . [Google Scholar]) as its theoretical foundation. The psychometric properties of the SCS–R were established using factor analysis, construct validity tests, as well as internal consistency and test–retest reliability. Five factors emerged: perceived behavioral control, positive attitude toward establishing consent, sexual consent norms, indirect consent behaviors, and awareness of consent. Results indicated that the SCS–R can be useful for examining a variety of research questions relating to sexual consent.     

Production efficiency and constraints on profit taxation and profit distribution in economies with Ramsey taxation

In economies with Ramsey taxation, decreasing returns to scale, and private ownership, we show that second-best production efficiency is desirable when the grouping of private firms induced by the profit taxation power of the government is at least as fine as the grouping of firms induced by the institutional rules of profit distribution in the economy. The classic results of Dasgupta and Stiglitz (Rev Econ Stud 39:87–103, 1972) (of firm-specific profit taxation) and Diamond and Mirrlees (Am Econ Rev 61:8–27, 1971a; Am Econ Rev 61:261–278, 1971b) and Guesnerie (A contribution to the pure theory of taxation, 1995) (of uniform 100 % profit taxation) follow as special cases of our model. Moreover, second-best analysis shows that optimal profit taxation is a substitute for optimal intermediate input taxation. In smooth economies, proportional, lump-sum, and affine modes of profit taxation are equivalent. We rework Mirrlees (Rev Econ Stud 39:105–111, 1972) counterexample, which is posed in the context of a non-smooth economy, to show that second-best production efficiency continues to remain desirable under an affine structure of profit taxation.