  Risk-limiting audits (RLAs) are techniques for verifying the outcomes of
large elections. While they provide rigorous guarantees of correctness,
widespread adoption has been impeded by both efficiency concerns and the fact
they offer statistical, rather than absolute, conclusions. We attend to both of
these difficulties, defining new families of audits that improve efficiency and
offer qualitative advances in statistical power.
  Our new audits are enabled by revisiting the standard notion of a cast-vote
record so that it can declare multiple possible mark interpretations rather
than a single decision; this can reflect the presence of marginal marks, which
appear regularly on hand-marked ballots. We show that this simple expedient can
offer significant efficiency improvements with only minor changes to existing
auditing infrastructure. We consider two ways of representing these marks, both
yield risk-limiting comparison audits in the formal sense of Fuller, Harrison,
and Russell (IEEE Security & Privacy 2023).
  We then define a new type of post-election audit we call a contested audit.
These permit each candidate to provide a cast-vote record table advancing their
own claim to victory. We prove that these audits offer remarkable sample
efficiency, yielding control of risk with a constant number of samples (that is
independent of margin). This is a first for an audit with provable soundness.
These results are formulated in a game-based security model that specify
quantitative soundness and completeness guarantees. These audits provide a
means to handle contestation of election results affirmed by conventional RLAs.
