In this paper, we question the common wisdom that more polarised voters' opinions imply larger policy polarisation. We analyse a voting model in which the source of the polarisation in voters' opinions is correlation neglect, that is, voters neglect the correlation in their information sources. Our main result shows that such polarisation in opinions does not necessarily translate to policy polarisation; when the electoral system is not too competitive (that is, when there is some aggregate noise in the election's outcome), then voters with correlation neglect may induce lower levels of policy polarisation compared with rational electorates.