TITLE Cryptographic election protocols for reweighted range voting & reweighted transferable vote voting AUTHOR Warren D. Smith DATE Sept 2005 ABSTRACT We describe a correct, ``verifiable,'' and ``coercion resistant'' cryptographically secure election scheme which takes $O(NC^k+V)$ (highly parallelizable) steps to process $V$ votes by $N$ voters in a $C$-candidate election, which for the election systems we shall be considering is best possible if $k=1$, and we achieve $k=1$ and/or $k=2$. Previous cryptographic election schemes had only been able to handle ``additive'' election methods such as Plurality, Approval Voting, Condorcet, or Borda count, or methods with ``anonymizable'' votes such as Instant Runoff Voting with few enough candidates $C$ so that votes were not expected to be uniquifiable (i.e. if $C! << V$). The new approach \emph{breaks} those barriers in the three most important special cases. First, we can handle the author's ``reweighted range voting'' (RRV) at least in the case when the number of possible scores for any given candidate is restricted to a small-enough set (such as the integer interval $[0,9]$) so that useful votes cannot be uniquely identified by consideration of the sum of its scores on the current winners. Second, we can handle Hare/Droop-reweighted STV (STV=\emph{s}ingle \emph{t}ransferable \emph{v}ote) provided we are willing to use inexact reweighting factors (truncated down to few bits of precision, e.g. to the nearest part in 120) with $k=2$. (For STV our runtime bound with $k=2$ probably is still best possible, but we have not proven this.) Third, we can also handle STV without reweighting and ``BTR-IRV.'' However, the new techniques still are not all-powerful because Woodall's DAC (Decreasing Acquiescing Coalitions) voting method still apparently cannot be handled. KEYWORDS Single Transferable Vote, reweighted range voting range voting, instant runoff voting, mixnets, coercion resistance, cryptographic security.