Very little. Whenever you refresh steemit.com you'd be using more bandwidth and processing on comments and votes (which are tallied the same way) than on tallying views. Counting is bread and butter for a computer. And counting the votes could even be done clientside (on the users phone or Web browser).
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That's why the chain would keep an ip address, so refreshing wouldnt count as a different page view. But you are right, an account would need to sign the transaction, so maybe it could come from the @null account or the interface owners account on behalf of users who aren't logged in.