On the Exact Amount of Missing Information that Makes Finding Possible Winners Hard

We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied model of incompleteness, the votes are given by partial orders over the candidates. In this context we can frame the problem of finding a possible winner, which involves determining whether a given candidate wins in at least one completion of a given set of partial votes for a specific voting rule. The Possible Winner problem is well-known to be NP-Complete in general, and it is in fact known to be NP-Complete for several voting rules where the number of undetermined pairs in every vote is bounded only by some constant. In this paper, we address the question of determining precisely the smallest number of undetermined pairs for which the Possible Winner problem remains NP-Complete. In particular, we find the exact values of t for which the Possible Winner problem transitions to being NP-Complete from being in P, where t is the maximum number of undetermined pairs in every vote. We demonstrate tight results for a broad subclass of scoring rules which includes all the commonly used scoring rules (such as plurality, veto, Borda, and k-approval), Copeland^alpha for every alpha in [0,1], maximin, and Bucklin voting rules. A somewhat surprising aspect of our results is that for many of these rules, the Possible Winner problem turns out to be hard even if every vote has at most one undetermined pair of candidates

KIPP Middle Schools: Impacts on Achievement and Other Outcomes

The Knowledge Is Power Program (KIPP) is a rapidly expanding network of public charter schools whose mission is to improve the education of low-income children. As of the 2012 -- 2013 school year, 125 KIPP schools are in operation in 20 different states and the District of Columbia (DC). Ultimately, KIPP's goal is to prepare students to enroll and succeed in college.Prior research has suggested that KIPP schools have positive impacts on student achievement, but most of the studies have included only a few KIPP schools or have had methodological limitations. This is the second report of a national evaluation of KIPP middle schools being conducted by Mathematica Policy Research. The evaluation uses experimental and quasi-experimental methods to produce rigorous and comprehensive evidence on the effects of KIPP middle schools across the country.The study's first report, released in 2010, described strong positive achievement impacts in math and reading for the 22 KIPP middle schools for which data were available at the time. For this phase of the study, we nearly doubled the size of the sample, to 43 KIPP middle schools, including all KIPP middle schools that were open at the start of the study in 2010 for which we were able to acquire relevant data from local districts or states. This report estimates achievement impacts for these 43 KIPP middle schools, and includes science and social studies in addition to math and reading. This report also examines additional student outcomes beyond state test scores, including student performance on a nationally norm-referenced test and survey-based measures of student attitudes and behavior

Campaign Management under Approval-Driven Voting Rules

Approval-like voting rules, such as Sincere-Strategy Preference-Based Approval voting (SP-AV), the Bucklin rule (an adaptive variant of $k$-Approval voting), and the Fallback rule (an adaptive variant of SP-AV) have many desirable properties: for example, they are easy to understand and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard even if the degree to which we need to affect the votes is small. Nevertheless, we identify a large class of scenarios that admit fixed-parameter tractable algorithms.Comment: 34 pages, 1 figur

Coverage, Matching, and Beyond: New Results on Budgeted Mechanism Design

We study a type of reverse (procurement) auction problems in the presence of budget constraints. The general algorithmic problem is to purchase a set of resources, which come at a cost, so as not to exceed a given budget and at the same time maximize a given valuation function. This framework captures the budgeted version of several well known optimization problems, and when the resources are owned by strategic agents the goal is to design truthful and budget feasible mechanisms, i.e. elicit the true cost of the resources and ensure the payments of the mechanism do not exceed the budget. Budget feasibility introduces more challenges in mechanism design, and we study instantiations of this problem for certain classes of submodular and XOS valuation functions. We first obtain mechanisms with an improved approximation ratio for weighted coverage valuations, a special class of submodular functions that has already attracted attention in previous works. We then provide a general scheme for designing randomized and deterministic polynomial time mechanisms for a class of XOS problems. This class contains problems whose feasible set forms an independence system (a more general structure than matroids), and some representative problems include, among others, finding maximum weighted matchings, maximum weighted matroid members, and maximum weighted 3D-matchings. For most of these problems, only randomized mechanisms with very high approximation ratios were known prior to our results

The Bidder's Curse

We employ a novel approach to identify overbidding in the field. We compare auction prices to fixed prices for the same item on the same webpage. In detailed board-game data, 42 percent of auctions exceed the simultaneous fixed price. The result replicates in a broad cross-section of auctions (48 percent). A small fraction of overbidders, 17 percent, suffices to generate the overbidding. The observed behavior is inconsistent with rational behavior, even allowing for uncertainty and switching costs, since also the expected auction price exceeds the fixed price. Limited attention to outside options is most consistent with our results.

Does money make people right-wing and inegalitarian? A longitudinal study of lottery winners

The causes of people’s political attitudes are largely unknown. We study this issue by exploiting longitudinal data on lottery winners. Comparing people before and after a lottery windfall, we show that winners tend to switch towards support for a right-wing political party and to become less egalitarian. The larger the win, the more people tilt to the right. This relationship is robust to (i) different ways of defining right-wing, (ii) a variety of estimation methods, and (iii) methods that condition on the person previously having voted left. It is strongest for males. Our findings are consistent with the view that voting is driven partly by human self-interest. Money apparently makes people more right-wing

Are Condorcet and minimax voting systems the best?

For decades, the minimax voting system was well known to experts on voting systems, but was not widely considered to be one of the best systems. But in recent years, two important experts, Nicolaus Tideman and Andrew Myers, have both recognized minimax as one of the best systems. I agree with that. This paper presents my own reasons for preferring minimax. The paper explicitly discusses about 20 systems, though over 50 are known to exist.Comment: 41 pages, no figures. The Introduction has been changed. Also fixed some version 6 errors in referencing subsection numbers in section