On the first day, most likely you'll treat that person to a sumptuous dinner then fork out cash to buy Movie Tickets. The cost of romance! There's no guarantee though that spending that kind of cash would get you instant love. There'll be more dates and dinners which will further thin your wallet. But how sure are you this person will stick by you when you are broke? Wouldn't it be better to split to the costs since your both on a quest to find Prince Charming or the "Queen of your heart?" Would you ask the person you are attracted to pay for some of those dinners?
On a date most people offer to pay rounds of drinks, but when it comes to a meal a woman should offer to pay and the man refuses in an ideal world. The man would then say "You can buy next time," or say they can buy coffee or drinks later. Personally men that don't pay on a first date are bad news and that chances are they won't get a second date unless they were friends already and had split bills. I think later on in a relationship couples can take it in turns to pay, I always offer, but I do expect the man to refuse, though I will pay for birthdays or special occasions. It also depends on who earns more and sharing the cost that way.
I think it is always better to split the bill. As I think both of them are there for the same purpose and when the goal is same why should only one person take the trouble of thinning their wallet.
I would just set expectations up front, by saying something like "hey I would like to treat you to a dinner at such and such place, if you're interested" - where you are already letting the other person know it's on you. Then hopefully if they want to go on some future dates, they will take the hint and also be up front and say something like "lets go see such and such movie, it's on me this time". I would be careful though about nickle and diming your date. They may not be as interested in you as you are in them, and it may take some time before they realize if they like you or not. In the mean time, they are giving up their free time to spend it with you and see how things go, don't expect them to foot the bill too. Oh and your date doesn't owe you anything if you two just don't hit it off or they ultimately aren't interested.
I think the best way would be to go dutch or to take turns paying. It's only appropriate to share the cost, instead of handing the burden to one person. It would make for an unhealthy relationship.
