Ordinal Bayesian Incentive-Compatible Voting Rules Withcorrelated Belief Under Betweenness Property

We consider social choice functions (SCFs) that are locally robust ordinal Bayesian incentive compatible (LOBIC) with respect to correlated priors. We model such priors using a betweenness property and assume the coexistence of both positively and negatively correlated priors. We introduce the notion of strong ordinal non domination (strong OND), which combines the notion of OND from Bhargava et al.(2015) with a monotonicity condition. Finally we show that strong OND is a sufficient condition for an SCF to be LOBIC in this framework