Left-authoritarian individuals, i.e. those with economically left, but culturally authoritarian policy preferences, have received increasing scholarly attention in the past years. While the left-authoritarian preference bundle is widespread among certain classes of society (the working class), West-European party systems often lack(ed) parties with a distinct left-authoritarian profile. How do left-authoritarians voters decide given this supply gap? Recent studies argue that whether left-authoritarians vote for left-libertarian or right-authoritarian parties depends on the salience they attach to the two different dimension of the policy space (Kurella & Rosset 2017; Lefkofridi et al. 2014; Spies 2013). We draw attention to two other, neglected factors that might shape their voting decision: Position misperception and left-right identification. On one hand, it should not be taken for granted that voters perceive party positions accurately, especially when parties blur their positions on one of the two dimensions. As a result, left-authoritarians might, incorrectly, perceive a party to hold positions similar to their own and decide to vote for this party. On the other hand, left-authoritarians differ in whether they identify with the left of right and we expect this ideological identity to exhibit powerful effects on voting decisions. Our study draws on a large-n (>10.000) panel survey dataset fielded during the campaign for the German election 2017 (GLES Campaign Panel), a context in which no viable party offered a left-authoritarian position. Rich data on individuals’ issue positions, the salience they attach to these issues and perceived party positions allow us to study the role of the different determinants of the left-authoritarian vote. Our study helps to illuminate how voters decide in a multidimensional policy space with constrained supply.