If a token is created as a standard eosio.token, what are some approaches for paying out dividends to token holders?
It's hard to visualize a dividend because to me that would imply paying others in EOS (a currency in which you do not directly control the inflation nor supply of).
With that said I see a few approaches. One would be just artificially increasing the supply of the token and issuing that over time. This would be an inflation effectively, but with a dividend type feeling due to the shareholders potentially receiving an equal share based on total stake.
Another approach could be where the dapp takes a cut each time the token is used for its utility or transferred to another user. This could create a fund from which dividends could be redistributed to everyone using the token (or just burning the token effectively causing deflation equally to all users).
From a psychological perspective, I think the end user would rather see the additional tokens coming in rather than not being able to see the tokens destroyed.
Dividends traditionally come from excess profit a company is taking in, so not all of the funds in that account would have to be redistributed.
You could also limit the accounts the dividend could apply to by creating a stake-like option like steemit used where users would elect to lock up their tokens for a longer period of time (weeks to months) in order to be eligible to receive the dividend based on how many tokens they've locked up.
By incentivizing users to lock up their tokens, this effectively reduces the float, or total amount of tokens that can be traded. In simple terms, less supply with the same demand leads to a price appreciation of the asset in question.