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Is the benefit of an additional glass of water greater or lesser than an additional one carat diamond? Why? Water is essential for life and diamonds are not.

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Lesser, for a one-carat diamond is worth between $4700 and $9300 depending on the quality of the cut. A glass of water is virtually free from the tap. Even all but the most expensive bottled waters costs less than 1/1000th of the cost of the diamond.

Of course, your question asks about benefits. Diamonds are not inherently valuable. Their value drops by over half once they leave the jewelry store. Their price is greatly driven up by a De Beers company monopoly and an advertising campaign. Before the 1930s, only the wealthy cared about diamond jewelry. Then advertisers pushed the idea of diamond engagement and wedding rings, with the mercenary demand that one's love be measured in the amount spent. Before then, couples more typically wore bands of gold, silver, or even iron. Men often didn't wear rings after the wedding, and women's engagement and wedding rings were one and the same, only switching hands after the ceremony.

Water will always be valuable since we need it to live. People will fight and die for it, most recently in Bolivia.

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This depends on the condition a person finds themself in when this choice is presented to them.  The marginal utility of a thing is solely in the "eye of the beholder."  Therefore, the marginal utility of these things will vary with the condition of the "consumer."

For a person who is very thirsty, the marginal benefit of the water is greater than that of the diamond.  If a person is truly dying of thirst, the marginal utility of the water is almost infinite while the diamond would be useless.

To a person who wants to propose marriage, however, the situation is reversed and the marginal utility of the diamond is much higher.

This is because marginal utility is defined as how much satisfaction a given person gets from consuming the object in question.  This amount will vary with the situation.

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