"Keep Summer Safe!"
Many Euros take three or four players. Sometimes two or five. Few play with six or more. There are many reasons (or at least, theories) as to why this is so, but I think one reason is that the games have a fixed amount of fun.
When Alhambra came out (two years ago), the reaction split — about half loved it, half hated it. How many people played often dictated the feeling. More players means less fun.
Usually, it's because you sit around during other players' turns. So the game takes the same amount of time, but you get to do less. The fun dilutes. These are 'fixed fun' games. Diplomacy doesn't dilute. Add or remove a player and you may change the balance (or variant), but each player gets the same amount of time to play.
This isn't a binary "Fixed vs non-fixed" choice; there's an elasticity of fun (as compared to number of players). In Puerto Rico, you lose control with players, but not as badly as Alhambra. Most games are in the middle, and designs that have fixed fun would be well advised to keep to lower limits.
Heckmeck im Bratwurmeck, Knizia's dice game, is a fixed fun game. I played it with four players, and loved it. You roll dice and keep all dice showing a single number, re-rolling the rest. But you can't keep a number you rolled before. Also, the dice show worms (as well as 1-5), and you need to keep at least one worm (valued at 5). If you have a value higher than the lowest available tile (which run 21-36), you can claim it. If you have the value equal to each player's most recently claimed tile, you steal it. If you crap out and have at least one tile, you return it (and sometimes remove the highest tile from the game). When no unclaimed tiles remain, you score (each tile shows 1-4 worms, which are points).
The reason I mention that it's a fixed fun game is that the box lists 2-7 players. Guess what you do when it's not your turn? Nothing. Ok, you watch dice tumble across the table. I'm surprised that anyone who played with six or seven liked the game. With seven, the game takes an hour (because one of the two 'timers' only functions when a player craps out and has a tile). But with 2-4, the game takes half as long, and each player gets more time with the dice.
It's a cute filler, nothing more. But I'd never dream of playing with a crowd.
[Since originally writing this, I've played several games two player. Needless to say, that's probably the best way to go. But even with a 3rd or fourth it's fine].