in city elections of the past, when the city councillors were elected through STV, the mayor was elected through AV.
If nothing else, this ensured that all contests used preferential voting, so made public education easy. Whether the voter chose to mark back-up preferences or not was up to the voter.
And sometimes under AV, back-up preferences had no effect -- no transfers were conducted because a candidate took a majority of votes on the first count, and usually the leader in the first count won in the end anyway same as who would have won under FPTP.
Otherwise, the election by PR did not affect election of mayor. still he or she would either be on the side of the majority of council or not - easy to see if party labels were used; if parties were not used, only time and votes in chamber would show whether the mayor was on side of majority or not.
Past reformers asked why we concentrate such attention on election of mayor when he or she has just one vote, same as any councillor, whose election we do not look much at.
I don't why -- perhaps just because it is exciting, the same reason why some people like the live or die result of singe-winner FPTP.
It is exciting to see just one winner emerge but it is not fair or democratic or inclusive.
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