Like many cryptocurrencies, the Steem economy includes the continual printing of new coins, a process which is often referred to as "inflation". This inflation is the source of value which underlies new upvotes. Steem inflation is currently around 8.5% per year (as at 2018).
For "Proof-of-Work" coins, like Bitcoin, the new coins generated with each block are awarded to miners. Miners use computing power to resolve the complex cryptographic puzzles needed to validate each new block of the blockchain. The new coins are their reward for undertaking this task.
Steem works differently. The amount of new coins generated is split between:
* Witnesses - for validating and securing the blockchain.
* Steem Power interest - Steem Power grows with interest over time.
* Reward pool - for rewarding new posts and comments.
All other things being equal, inflation (an increase in the supply of coins) reduces the value of the existing coins. As such, it can be argued that the value of the new coins, and thus the value of upvotes, is provided by a reduction in the value of existing coins.
Based on this argument, it is the existing Steem holders who fund the reward system, in proportion to their Steem holdings.
However it should be noted that a large proportion (the majority by value) of Steem holders do not vote on posts and take no active part of the reward pool. A large part of this is due to no voting by the Steemit team's holdings, as well as liquid Steem held on exchanges. This acts as a large subsidy, providing a large part of the value of each upvote.
So it can also be argued that active Steem holders only pay a proportion of the cost of upvotes, with the Steemit team and non-active Steem holders providing the majority.