POSTER: A Card-Based Protocol that Lets You Know How Close Two Parties are in their Opinions (agree/disagree) by Using a Four-Point Likert Scale

Abstract

Card-based protocols are commonly used for scenarios where two parties need to perform an AND operation. These protocols are known for providing a non-embarrassing way to confess love, as the other party cannot determine whether the input is 0 or 1. This paper proposes a new card-based protocol that involves four cards distributed between two parties, and is based on the assumption that all four values are accepted. The protocol asks both parties to indicate how close their opinions are on a four-point scale (0 = not at all disagree, 1 = somewhat disagree, 2 = somewhat agree, and 3 = strongly agree), which is commonly used in surveys. The protocol consists of three patterns: complete agreement, approximate agreement (cases with inputs {0,1} or {2,3}), and disagreement. The results are only known to the parties, and the inputs are kept secret from the third party. It should be noted that our Likert scale excludes the neutral response “undecided”. Furthermore, the case of our proposal has the algebraic structure as one of the association schemes with 4 points.