Ticket for gas

My insightful sister was wondering. Why doesn't the government just sell tickets with different nominal values to the BBM consumers? Those with high income should buy one ticket 5 times as much as those with low income, for example. The problem with this type of mechanism is, as I told her, monitoring. Mr. Rich will ask Mr. Poor next door to buy tickets for him. With some incentives, Mr. Poor will do it happily. Moral hazard and adverse selection at play. (Still this is worth elaborating. After all, even the compensation mechanism offered by the government is not free from such problems).

Addendum:
My sister responded again:

I got the point of difficulty in monitoring. In fact what I was particularly wondering is how to make people that use public transport, regardless of being poor or rich, pay bbm/liter less than those use private cars. The justification made is simply that people using public transport use up much less space of the road and do not get as much convenience as people using private vehicle. I am fully aware of the absurdity of effort to identify who the poor or rich are in Indonesia.

I mentioned about ticketing for buses through which government gives subsidy to the public transport users, i.e: users buy bus tickets at Rp. X, then the bus operator can reimburse the tickets at Rp X+Y. ticketing system has been applied for KRL (have no info of how it works). Unfortunately, as you said, for ticketing, there is always an issue of ticket faking. Now, what about allocating oil stations for buses where oprators can get cheaper bbm?

To which I replied:

Nice thoughts. On your last question. We sure hope the bus drivers do not have some evil pact with some guy somewhere: fill up their tanks repeatedly, and go sell somewhere else at higher prices. Arbitrage at play.

And I told her, please keep stimulating such good ideas; and don't get tired by economists' skeptical starting points in looking at things -- they are skeptical.