[Analemma_]

On a per-dish basis, yes. But dishwashers are a classic Jevons paradox: once you factor in that the convenience of having one increases your dish usage versus the counterfactual of having to hand wash everything you use, the comparison is less straightforward.

[DamonHD]

My family does not, so far as I can tell, use a different number of dishes because of the presence of a dishwasher. The kids almost never wash(ed) up, so it makes/made no difference to them for example. And I loathe washing up, but I always use as few dishes etc as I reasonably can simply from a sustainability point of view. And I ensure that the dishwasher is as full as reasonably possible before being run, and run at the best time from a carbon/cost point of view.

[Sammi]

If you're a single person living in a flat in a city, then you can get in the habit of rinsing your tableware right after using when stuff still easily comes off, and therefore not use much effort at all on washing, and you just reuse the same tableware over and over. This is common and the reason why dishwashers aren't much needed for some.