Word/phrase for getting people to do something because people in that bucket/group exhibit positive behaviours

Question

Scenario: We are a supermarket that has a rewards card program and customers using this program exhibit positive behaviours (e.g. increased spending at our stores). It is assumed this is beacuse they are more engaged in the brand.

We want to increase spending for non-rewards customers (they generally spend less), therefore it has been suggested that we force everyone to get a rewards card in the hopes it will increase their spending too.

However these customers aren't as engaged in the brand, therefore their spending may not increase as expected.

To summarise, is there a word or phrase for the following sort of logic/process of thinking?

Trying to get people into a certain bucket/group because that bucket/group exhibits desired behaviours and expecting them to behave the same, even though they are different types of people.

This is of course doomed to fail as these are different types of customers and aren't going to suddenly change their behaviour.

A possible usage sentence may be (it's hard for me to guess since I don't know the word/phrase)

Although getting more people to use our rewards card to increase spending sounds like it would work, I think your idea falls victim to the following_____________.

Answer 1

There's an adage that covers the whole scenario:

You can lead a horse to water, but you can't make him drink.

CED explains:

saying ​ used to emphasize that you can make it easy for someone to do [/ encourage them to do] something, but you cannot force them to do it

Answer 2

The word would be 'compel'. You want to 'compel' people to join your group by offering 'compelling' rewards.

Compel: To have a powerful and irresistible effect, influence, etc.

Compel can have undertones of using force, but in regards to a rewards program they are not being forced to join they should probably feel influenced, rather than forced.