We propose a randomized social choice rule called Mixed Integrated Veto (MIV) with metric distortion of $5/2$, improving the previous best upper bound of $2.75271$. MIV is the equal mixture of Maximal Lotteries and Integrated Veto, a new rule built on the Simultaneous Veto process of Kizilkaya and Kempe. Rather than returning the candidate surviving longest, Integrated Veto assigns each candidate probability proportional to its average score over the whole process.

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