Pattern Matching Encryption, Strategic Equivalence of Range Voting and Approval Voting, and Statistical Robustness of Voting Rules

We present new results in the areas of cryptography and voting systems. 1. Pattern matching encryption: We present new, general definitions for queryable encryption schemes – encryption schemes that allow evaluation of private queries on encrypted data without performing full decryption. We construct an efficient queryable encryption scheme supporting pattern matching queries, based on suffix trees. Storage and communication complexity are comparable to those for (unencrypted) suffix trees. The construction is based only on symmetric-key primitives, so it is practical. 2. Strategic equivalence of range voting and approval voting: We study strategic voting in the context of range voting in a formal model. We show that under general conditions, as the number of voters becomes large, strategic range voting becomes equivalent to approval voting. We propose beta distributions as a new and interesting way to model voter’s subjective information about other votes. 3. Statistical robustness of voting rules: We introduce a new notion called “sta- tistical robustness” for voting rules: a voting rule is statistically robust if, for any profile of votes, the most likely winner of a sample of the profile is the winner of the complete profile. We show that plurality is the only interesting voting rule that is statistically robust; approval voting (perhaps surprisingly) and other common voting rules are not statistically robust

Pattern matching encryption, strategic equivalence of range voting and approval voting, and statistical robustness of voting rules

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 119-123).We present new results in the areas of cryptography and voting systems. 1. Pattern matching encryption: We present new, general definitions for queryable encryption schemes - encryption schemes that allow evaluation of private queries on encrypted data without performing full decryption. We construct an efficient queryable encryption scheme supporting pattern matching queries, based on suffix trees. Storage and communication complexity are comparable to those for (unencrypted) suffix trees. The construction is based only on symmetric-key primitives, so it is practical. 2. Strategic equivalence of range voting and approval voting: We study strategic voting in the context of range voting in a formal model. We show that under general conditions, as the number of voters becomes large, strategic range-voting becomes equivalent to approval voting. We propose beta distributions as a new and interesting way to model voter's subjective information about other votes. 3. Statistical robustness of voting rules: We introduce a new notion called "statistical robustness" for voting rules: a voting rule is statistically robust if, for any profile of votes, the most likely winner of a sample of the profile is the winner of the complete profile. We show that plurality is the only interesting voting rule that is statistically robust; approval voting (perhaps surprisingly) and other common voting rules are not statistically robust.by Emily Shen.Ph.D

Crowdsourcing for Participatory Democracies: Efficient Elicitation of Social Choice Functions

We present theoretical and empirical results demonstrating the usefulness of voting rules for participatory democracies. We first give algorithms which efficiently elicit \epsilon-approximations to two prominent voting rules: the Borda rule and the Condorcet winner. This result circumvents previous prohibitive lower bounds and is surprisingly strong: even if the number of ideas is as large as the number of participants, each participant will only have to make a logarithmic number of comparisons, an exponential improvement over the linear number of comparisons previously needed. We demonstrate the approach in an experiment in Finland's recent off-road traffic law reform, observing that the total number of comparisons needed to achieve a fixed \epsilon approximation is linear in the number of ideas and that the constant is not large. Finally, we note a few other experimental observations which support the use of voting rules for aggregation. First, we observe that rating, one of the common alternatives to ranking, manifested effects of bias in our data. Second, we show that very few of the topics lacked a Condorcet winner, one of the prominent negative results in voting. Finally, we show data hinting at a potential future direction: the use of partial rankings as opposed to pairwise comparisons to further decrease the elicitation time