The aggregated excess demand function and other aggregation procedures

Summary Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set ofn2 commodities to all of the 2 ⁿ –(n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k2 candidates over a space of n2 issues. The theorem characterizes the sincere elecion rankings of thek candidates over all of the 2 ⁿ –1 subsets of one or more issues. Both theorems have the same kind of conclusion; anything can happen. By demonstrating the mathematical reasons for these conclusions and by recalling related, recent results from statistics, voting, and economics, it is argued that this anything can happen conclusion is the type one must anticipate for aggregation procedures; particularly for the processes commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.I am pleased to acknowledge conversations with L. Hurwicz, A. Mas-Colell and C. Simon about this material. In particular, I want to thank J. Jordan for his several helpful suggestions. Also, I benefited from comments made at meetings and seminars where these results were presented; this includes a June, 1990, conference in Stockholm, Sweden. Some stylistic suggestions were made by Arvid and Padon Kalinen. This research was supported, in part, by NSF Grant IRI-8803505.     

Mathematical structure of voting paradoxes

Summary. A theory is developed to identify, characterize, and explain all possible positional and pairwise voting outcomes that can occur for any number of alternatives and any profile. This paper describes pairwise voting where new results include explanations for all paradoxes, cycles, conflict between Borda and Condorcet rankings, differences among procedures using pairwise votes (such as the Borda Count, Kemeny's method, and the Arrow-Raynaud rule), and discrepancies among the societal rankings as candidates are dropped or added. Other new results include new relationships among the Borda and Condorcet "winners" and "losers." The theory also shows how to construct all supporting profiles. The following companion paper does the same for positional methods.     

The representation problem and the efficiency of the price mechanism

It is shown in this paper that the way in which an allocation is represented (net trades, final allocation, etc.) can affect the design of any realizing mechanism or incentive compatible system. The reason is that a poor choice of representation may be imposing superfluous conditions and demands upon the realizing mechanism. So, in this paper a technique is developed to (1) find the optimal representation of an allocation, and (2) to characterize the associated, realizing mechanisms. Although this approach is designed to be applied to any smooth economic model, it is illustrated and motivated here by applying it to the price mechanism. More specifically, there are assertions in the literature by Mount and Reiter and by Hurwicz that the price mechanism is informationally efficient over the class of Pareto seeking mechanisms. These proofs are incomplete because they consider only one choice of representation for the Pareto allocations. We use this technique to (a) reassert the dimensional efficiency of the price mechanism, (b) compare mechanisms for spaces of economics with and without externalities, (c) characterize for the space of quadratic functions the other dimensionally efficient allocation concepts, and (d) characterize those two agent economics where the price mechanism is dimensionally efficient.     

Making bottom-up and top-down processes meet in public innovation

Innovations in an organisation derive from multiple sources. In the public sector, users and the policy sphere provide important but often unconnected impulses for innovation. These impulses are transmitted to the organisation by grassroots employees who interact with users and managers who implement policy requirements. The paper examines the actors and activities that coordinate bottom-up and top-down initiatives and promote their development into innovations. It creates a theoretical framework that combines the views of employee-driven innovation and strategic reflexivity and supplements them with an analysis of coordination in innovation processes. The functioning of this framework is illustrated in the context of children's day care services. The results highlight the central role of middle managers and provide new knowledge regarding their ‘bridging’ activities in innovation. The adjustment of bottom-up and top-down processes requires the personal involvement of managers, and the creation of communication arenas, networks and mediating tools.     

Some Surprising Properties of Power Indices

While it is troubling when power-index values change with the index, the problem is more severe: Different indices can generate radically different rankings. For example, a 15-player game exists with over a trillion different strict index rankings of the players. In contrast, with a fixed number of players certain indices always share the same ranking: e.g., the Shapley and Banzhaf rankings agree with three players, but they can have opposite rankings with more players. It is explained why index outcomes can be sensitive to assumptions and to when players leave a game. Journal of Economic Literature Classification Numbers: C71, D71.     

Mathematical structure of voting paradoxes

Summary. A theory is developed to explain all positional voting outcomes that can result from a single but arbitrarily chosen profile. This includes all outcomes, paradoxes, and disagreements among positional procedure outcomes as well as all discrepancies in rankings as candidates are dropped or added. The theory explains why each outcome occurs while identifying all illustrating profiles. It is shown how to use this approach to derive properties of methods based on pairwise and positional voting outcomes. Pairwise voting is addressed in the preceding companion paper [15]; the theory for positional methods is developed here.     

Unsettling aspects of voting theory

Summary. Voting procedures are known to be plagued with a variety of difficulties such as strategic voting, or where a voter is rewarded with a better election outcome by not voting, or where a winning candidate can lose by receiving more support. Once we know that these problems can occur, the next objective should be to completely understand how, why, and where they arise. Namely, for each election procedure, the new goal is to determine when such problems can occur, all voter types who can cause these difficulties, and the actions they must take. This paper develops an easily used approach to handle all of these issues for standard voting methods. New intuitive explanations for these various oddities follow from this approach. Received: August 14, 2002 ; revised version: September 4, 2002 RID="*" ID="*"My thanks to Richard Barrett and, in particular, to Hannu Nurmi for corrections, several useful comments, and suggestions they made about earlier versions. Also, my thanks to a referee for calling some excellent references to my attention. An earlier draft was presented at the 2002 Public Choice Society meeting. This research was supported by an NSF grant.     

Negative externalities and Sen’s liberalism theorem

Summary. Sen’s seminal, negative theorem about minimal liberalism has had a profound effect on economics, philosophy, and the social sciences. To address concerns raised by his result, we show how Sen’s assumptions must be modified to obtain positive conclusions; e.g., one resolution allows an agent to be decisive only if his choice does not impose “strong negative externalities” on others. We also uncover a significantly different interpretation of Sen’s societal cycles: rather than describing the rights of individuals to choose, the cycles identify when these choices impose difficulties on others. Other ways to address Sen’s difficulties come from game theory.Received: 14 October 2004, Revised: 7 March 2005, JEL Classification Numbers: D71, C70, D62.Donald G. Saari: Correspondenc toThe research of D. Saari was supported by NSF grant DMI-0233798. Our thanks to P. Hammond for suggesting some useful references. Some of our joint results were reported in Brunel (now Petron) (1998).     

Income Distribution across Ethnic Groups in Malaysia: Results from a New Social Accounting Matrix

A new social accounting matrix is constructed for Malaysia for the year 2000 to analyze sources of income inequality among ethnic groups in Malaysia. The analysis reveals that income inequality can be decomposed into the interaction of: (i) hourly wages; (ii) working hours per week; and (iii) number of dependents per household. The results of the analysis suggest that occupational differences are the main factor contributing to wage inequality in Malaysia. Ethnic Malays tend to work in low‐wage industries while ethnic Chinese and Indians are more likely to work in higher‐wage industries.     

The geometry of Black''s single peakedness and related conditions

By using geometry to analyze all three candidate profiles satisfying Black's single peakedness constraint, we characterize all associated election behavior. The same analysis is applied to related profile constraints where some candidate never is top-ranked, or never bottom ranked.