A reminder- plain Approval Voting can directly violate head to head majority
rule.

Extreme example--
51 AB
49 B

With AV, B gets 100, A gets 51, B wins.
With head to head, A obviously wins 51 to 49.
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A slightly less extreme example--
14 CE
6   CD

45 DC

29 EC
6   ED

With AV, C gets 94, D gets 57, E gets 49, C wins.
With head to head, D beats C, 51 to 49 and D beats E 51 to 49. D wins.

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