This poll was a little bit of a trick question. The bigger question is either "who put you in charge?" or "why should we allocate water according to a I-win-you-lose vote when that water can be allocated in a market?"
I think that most of you will agree that a dictator-type decision is not a good idea (either because dictators are corrupt or make mistakes in deciding what's good for all of us), but the case against a majority rule is a little more subtle.
First, there is the fact that political decisions should only be used for collective goods (e.g., funding a fire department), but not for private goods (e.g., let's vote on who gets the water for a pool/business/farm).
Second, there is the complication of "environmental water" in this poll. A majority of people are willing to vote for more water to the environment, which means less water for other -- private -- activities, more costs (to replace the lost water), lower profits, and/or lower happiness. So there's a cost to that reallocation that would be better represented by willingness to pay (I'll pay $1 for the environment but $10 for more food), which would allow voters to express their private value of water instead of a simple "yea" that is just the same as any other "yea."
But what about the social -- or collective -- value of water for the environment? Well, here's where it gets interesting. Two voters who assign a value of $5/each to environmental flows could put their money together to vote $10 for the environment that they both appreciate. Two businessmen with $5 values could not, since they each want the water for their own private uses.
From this example, you can see that environmental voters should prefer money votes. The strange thing is that they prefer a political process. I think that reflects a decision to garner the [weak] support of the masses signing petitions outside the Whole Foods and avoid a discussion of the value of water in other uses.
Bottom Line: Everyone wants something for nothing, but they will have to pay up when the quantity of something approaches nothing.