I feel I understand how bitcoin works as I have rebuilt it multiple times at this point, although I can understand why it was unclear what I meant. When I say bitcoin is like the government, I meant it in a very general sense with nodes acting like the citizens within the population.  I am not referring to transactions acting as votes but rather nodes accepting/confirming the longest chain as their vote.

 Citizens(nodes) do their jobs everyday to contribute to the economy which is the ongoing macro system(make and distribute transactions). Presidents(nodes) are randomly selected to group transactions for the next block through attempts at solving the POW function for that block.  Just like a president a citizen(node) is selected for a brief time period to make potential decisions for the networks next economic state . The difference being instead of 4 years of decisions it is building 1 block/proposal worth of decisions.

When it comes to the analogy, I am referring less to the specifics of the voting/election aspect and more to how it is unlikely for a system to be represented accurately from a single point or origin. A president is selected and then treated as a temporary origin point for decisions. The population can always rebel(accept another chain), however, the problem more so lies in the fact that the “president “ only has access to a single market perspective for forming proposals.

This means each time a proposal is made it is only coming from the perspective of that position in the network thus limiting the systems ability to build the most efficient block for adapting to market conditions. Focusing on network communication you would be able to instead decide on the best potential block for the network rather than the block of the first person that solves the POW.

In this analogy you could take it even farther and say that mining pools are similar to political parties how the network uses mining pools to group candidates and simplify the selection process but I will admit it's a bit of a stretch.

To summarize:
POW:
Selects proposal based on what node is making it.(selects potential proposal based on node who first solved POW)

Ideal:
Selects proposal based on best proposal for the current conditions
(Selects node based on best potential proposal)

Transactions = participation in the economy
Proposals =transitions system to next economic/market state
Nodes = citizens
President = node/citizen who solves POW first that term(block)
Votes = which proposal/chain a node is willing to confirm/using