In Canada, there is a very popular form of local fundraising called the “50-50.” It works like a raffle. 50% of the total money collected is given to one of the participants. And the other 50% goes to the cause of the fundraising. Of course, the odds of winning are weighted proportionately by the donation given. Lately, it has been wrongly reported that this is a bad deal. The first argument given is regarding the lower incentives to gamblers. Las Vegas slot machines are set to 97% return ratios. Meanwhile, a 50-50 lottery only gives a 50% return ratios.

The second reason that is given to consider this lottery a bad idea is because it makes a subpar charitable donation. Only 50% of the donation will go charitable cause. This is considered a very poor ratio in the philanthropic world. The bare minimum accepted in somewhere around the 60%. Therefore the combination of these two poor choices does not boost the overall value. Instead, what they do is to reinforce the bad value of both poor choices.

The intuition previously presented is greatly wrong.  Yes, a 50-50 lottery is not a charity drive. However, there have been lots of studies regarding the efficacy of lotteries both theoretically and empirically. John Morgan, Professor of Economics at Berkeley, has elegantly shown; under standard assumptions that lotteries outperform the simple ask. That means that without any risk-loving or lottery-loving behavior, this 50-50 lottery outperform voluntary contributions.The reason why lotteries obtain higher levels of public-goods provision than a voluntary contributions mechanism (VCM) is because the lottery rules introduce additional private benefits from contributing.

Here is the proper intuition. In the standard VCM, there is a free-riding tendency. That means that people do not contribute as much as we would like because they do not fully recognize how their gifts affect others (i.e., they do not fully recognize the positive externality they impose on others).  In this case, people give too little to the charity compared to what is best for everyone. However, when you introduce a lottery (for example, for every dollar you give you receive one ticket for a $1,000 prize) this free-riding effect is counteracted.  This is because when the level of giving is increased by a dollar, the chances of winning the lottery increase as well.  At the same time, everyone else’s chances decrease.  In this way, by giving one more dollar you impose a negative externality on others through the lottery, since their possibilities of winning decrease by the same amount. This effect, of course, does not account for when simply giving money to charity.

So, in the end, on a VCM the negative externality that is imposed by all the donors is sometimes counterweighted by the positive externality. Unfortunately, the level of overall money gave lowers because of the free-rider problem. Once a lottery in introduced the overall money gave increases, as well as the incentives to participate. Of course, a love of gambling, etc., can increase this effect.