X THEN X: Manipulation of Same-System Runoff Elections

Do runoff elections, using the same voting rule as the initial election but just on the winning candidates, increase or decrease the complexity of manipulation? Does allowing revoting in the runoff increase or decrease the complexity relative to just having a runoff without revoting? For both weighted and unweighted voting, we show that even for election systems with simple winner problems the complexity of manipulation, manipulation with runoffs, and manipulation with revoting runoffs are independent, in the abstract. On the other hand, for some important, well-known election systems we determine what holds for each of these cases. For no such systems do we find runoffs lowering complexity, and for some we find that runoffs raise complexity. Ours is the first paper to show that for natural, unweighted election systems, runoffs can increase the manipulation complexity

The Complexity of Manipulating kk-Approval Elections

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems

Complexity of Manipulative Actions When Voting with Ties

Most of the computational study of election problems has assumed that each voter's preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative actions on elections where voters can have ties, extending the definitions of the election systems (when necessary) to handle voters with ties. We show that for natural election systems allowing ties can both increase and decrease the complexity of manipulation and bribery, and we state a general result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201

Proportionality in Election Systems

Purpose This essay introduces first an overview over the most common election systems and, in particular the Swedish election system. The main purpose is then to examine how well the current system in Sweden performs with respect to proportionality and then to analyse how a more proportional system can be achieved. Method The Swedish election system is analysed using a computer simulation method. Based on a large number of simulated election outcomes is the degree of proportionality examined. In the simulations take the main values of the Swedish election system, namely the number of constituencies, the numbers of adjustment seats and the most important value in the technique of distributing mandates, different values. Conclusion: When the constituencies are of equal size, a number of 10 to 15 constituencies give the most proportional result. For the current distribution of constituencies, a value between 1.2 and 1.3 on the first divisor is preferred. A large number of adjustment seats leads in general to a more proportional result

Seeking votes - the political economy of expenditures by the Peruvian Social Fund (FONCODES), 1991-95

President Alberto Fujimori created the Peruvian social Fund (FONCODES) in 1991 with the stated objectives of generating employment, helping to alleviate poverty, and improving access to social services. The author uses province-level data on monthly expenditures, socio-economic indicators, and electoral outcomes to analyze political influences on the timing and geographic distribution of FONCODES expenditures between 1991 and 1995. He finds that: 1) FONCODES expenditures increased significantly before elections. 2) FONCODES projects were directed at poor provinces, as well as provinces in which the marginal political impact of expenditures was likely to be greatest. The results are robust to many specifications and controls. The Peruvian data thus support predictions made in the literature on political business cycle as well the literature on political influences on the allocation of discretionary funds.Decentralization,Environmental Economics&Policies,Parliamentary Government,Health Economics&Finance,Election Systems,Health Economics&Finance,Environmental Economics&Policies,Parliamentary Government,Election Systems,Business in Development

The Complexity of Online Manipulation of Sequential Elections

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a framework, in which manipulators can see the past votes but not the future ones, to model online coalitional manipulation of sequential elections, and we show that in this setting manipulation can be extremely complex even for election systems with simple winner problems. Yet we also show that for some of the most important election systems such manipulation is simple in certain settings. This suggests that when using sequential voting, one should pay great attention to the details of the setting in choosing one's voting rule. Among the highlights of our classifications are: We show that, depending on the size of the manipulative coalition, the online manipulation problem can be complete for each level of the polynomial hierarchy or even for PSPACE. We obtain the most dramatic contrast to date between the nonunique-winner and unique-winner models: Online weighted manipulation for plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive case) and NP-hard (destructive case) in the unique-winner model. And we obtain what to the best of our knowledge are the first P^NP[1]-completeness and P^NP-completeness results in the field of computational social choice, in particular proving such completeness for, respectively, the complexity of 3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition manipulation of veto elections.Comment: 24 page

At-Large Elections and Vote Dilution: An Empirical Study

The 1982 amendments to the Act, however, have remained a subject of controversy. Opponents of the Act misperceive municipal at-large electoral systems, believing they provide as much minority representation as single-member district systems. This Note addresses that misperception with data showing that at large schemes provide significantly less minority representation than other schemes. The various standards used by federal courts in reviewing the constitutionality of at-large election systems are outlined in Part I. Part II sets forth an analysis of Congress\u27s response to the judicial ambivalence toward at-large elections- the 1982 amendments to section 2 of the Voting Rights Act. Part III presents empirical data illustrating that, generally, blacks are significantly more underrepresented on city councils in cities with at-large election systems than in cities with district systems. Part IV discusses the implications of the Note\u27s empirical findings in light of the congressional amendments to the Voting Rights Act. The Note concludes that the congressional reimposition of the results standard for proving at-large election systems discriminatory was a necessary step forward because municipal at-large election systems remain systematically underrepresentative of significant population groups

Solving hard problems in election systems

An interesting problem in the field of computational social choice theory is that of elections, in which a winner or set of winners is to be deduced from preferences among a collection of agents, in a way that attempts to maximize the collective well-being of the agents. Besides their obvious use in political science, elections are also used computationally, such as in multiagent systems, in which different agents may have different beliefs and preferences and must reach an agreeable decision. Because the purpose of voting is to gain an understanding of a collection of actual preferences, dishonesty in an election system is often harmful to the welfare of the voters as a whole. Different forms of dishonesty can be performed by the voters (manipulation), by an outside agent affecting the voters (bribery), or by the chair, or administrator, of an election (control). The Gibbard-Satterthwaite theorem shows that in all reasonable election systems, manipulation, or strategic voting, is always inevitable in some cases. Bartholdi, Tovey, and Trick counter by arguing that if finding such a manipulation is NP-hard, then manipulation by computationally-limited agents should not pose a significant threat. However, more recent work has exploited the fact that NP-hardness is only a worst-case measure of complexity, and has shown that some election systems that are NP-hard to manipulate may in fact be easy to manipulate under some reasonable assumptions. We evaluate, both theoretically and empirically, the complexity, worst-case and otherwise, of manipulating, bribing, and controlling elections. Our focus is particularly on scoring protocols. In doing so, we gain an understanding of how these election systems work by discovering what makes manipulation, bribery, and control easy or hard. This allows us to discover the strengths and weaknesses of scoring protocols, and gain an understanding of what properties of election systems are desirable or undesirable. One approach we have used to do this is relating the problems of interest in election systems to problems of known complexity, as well as to problems with known algorithms and heuristics, particularly Satisfiability and Partition. This approach can help us gain an understanding of computational social choice problems in which little is known about the complexity or potential algorithms. Among other results, we show how certain parameters and properties of scoring protocols can make elections easy or hard to manipulate. We find that the empirical complexity of manipulation in some cases have unusual behaviors for its complexity class. For example, it is found that in the case of manipulating the Borda election of unweighted voters with an unbounded candidate cardinality, the encoding of this problem to Satisfiability performs especially well near the boundary cases of this problem and for unsatisfiable instances, both results contrary to the normal behavior of NP-complete problems. Although attempts have been made to design fair election systems with certain properties, another dilemma that this has given rise to is the existence of election systems in which it is hard to elect the winners, at least in the worst case. Two notable election systems in which determining the winners are hard are Dodgson and Young. We evaluate the problem of finding the winners empirically, to extend these complexity results away from the worst case, and determine whether the worst-case complexity of these hard winner problems is truly a computational barrier. We find that, like most NP-complete problems such as Satisfiability, many instances of interest in finding winners of hard election systems are still relatively simple. We confirm that indeed, like Satisfiability, the hard worst-case results occur only in rare circumstances. We also find an interesting complexity disparity between the related problems of finding the Dodgson or Young score of a candidate, and that of finding the set of Dodgson or Young winners. Surprisingly, it appears empirically easier for one to find the set of all winners in a Dodgson or Young election than to score a single candidate in either election