It always starts the same way -- you're at a nice bar with your special lady friend, and you order a drink. How wonderful that first drink will be after a long day! But then your drink arrives, and it's more sculpture than libation -- a rocks glass with a millimetre of spirits beneath a giant, specially crafted ice sphere. You ordered a drink, but you got a bowling ball in a cup.
Picture: Christophe Richard
The idea being that the larger piece of ice will melt slower, and dilute the spirit less. And that's true. That also means it will cool the drink less. As Kevin Liu says on Serious Eats:
Whenever we talk about ice and chilling, it's important to remember that there is no chilling without dilution. The vast majority of the chilling power of ice comes from the heat of fusion -- that is, the heat ice sucks up from its surroundings when it turns into water. And since it takes 80 times as much energy to melt a gram of ice as it does to raise a gram of solid ice one degree in temperature, any significant change in the temperature of a drink correlates directly with the amount of ice melted.
Moreover, a splash of water is said to make the flavour of the whisky or scotch "bloom", if you're particularly interested in exploring the reaches of your palate. Of course, serious scotch aficionados probably aren't dunking cubes from plastic freezer trays in their rare spirits, but they do sometimes add a splash of water.
Plus, if a large piece of ice sits exposed to air as you drink it, the exposed area will melt without cooling the drink (instead cooling the surrounding air). Personally I enjoy the melting ice as the drink progresses. When the liquor is gone, the ice water gives you something to sip on, if it's not appropriate or too soon to order another drink. Hit the link for more myths about cocktail ice.
Cocktail Science: 5 Myths about Ice, Debunked [Serious Eats]