Can You Solve this Ice Diamond Riddle? ft. Vsauce’s Michael Stevens

It should go up, I think. 

Generally speaking, mass in water will displace the water, causing it to rise. 

In this particular case, though, the mass gradually melts, so the mass of the ice cube will get smaller, and therefore displace less water. 

But what you have to remember is that it's ice. It's melting and turning into water, adding itself to the container of water. So while the displacement is going down, the amount of water is going up. 

Another way to think about it is to assume there was no water in the glass to start with. You put the ice cube in it and let it melt. Now the glass has water in it. Same principle.