Could someone review my logic?
Let's consider a policy I believe would benefit people, such as a sugar tax. Typically, under such a tax, the cost is usually passed on to the consumer (literature shows ~70% of tax is passed on). Now, imagine there's an entity, like a company or interest group, that strongly opposes this policy because it would cut their profits by an amount represented as $X in Net Present Value (NPV). Ordinarily, they would be willing to spend $X on lobbying efforts to sway lawmakers and prevent the policy's implementation. In reality they spend less than $X because 1) there is an opportunity to free-ride other similar companies 2) there is a chance that they spend $X and the government still passes the policy.
Let's say I am a wealthy billionaire with a vision for social good. I offer the aforementioned interest group $X, and together we proceed to implement the policy. However, is it reasonable to assume that the interest group would utilize the $X payment to lower the soda's price? It seems unlikely. A rational profit-maximizing company would likely still shift the burden of the tax onto consumers. This is because, despite the cash infusion of $X, the company's optimization behavior under the tax remains consistent with what it would have been without the payout.
So, how does this play out in reality? Rough estimates indicate that the food and beverage industry spent an extra $50 million on lobbying against a national sugar tax in 2009. According to a 2012 Health Affairs article, a tax of one cent per ounce on sugary beverages could prevent around 26,000 premature deaths over a decade. Assuming a constant rate of 2,600 lives saved annually, and applying a social discount rate of 3.5% (chosen somewhat arbitrarily), the cumulative lives saved due to the soda tax would be 74,285. This leads us to a cost of $50 million divided by 74,285 lives, resulting in approximately $673 per life saved.
Consequently, it appears to be highly cost-effective to simply buy out the soda and beverage industry. Although we haven't factored in the consumer surplus lost due to the sugar tax, even after considering this aspect, the policy seems to be a significant improvement for overall welfare. This is especially true considering the high price elasticity of sugar.
TLDR:
If a policy is opposed by a small interest group but would benefit the entire world, then it appears optimal to just pay off the small interest group so that we can implement the policy. First approximation for sugar tax shows a cost-effectiveness of $673 per life saved in the US, and likely lower for elsewhere in which there is a smaller beverage lobby.
This is directionally correct and is a known result in the political economy literature. Analogous techniques have been used in a range of contexts to overcome collective action problems. There is more detail in e.g. this book and my general overview here: https://forum.effectivealtruism.org/posts/o8TfAbYgDGKbeu6Da/vetocracy-reduction-and-other-coordination-problems-as
tl;dr [edited mainly for tone] - although in general buying out lobbyists can work, the proposal doesn't use the right numbers in calculating its costs.
Hi, in your first paragraph you implicitly identify that there are two important and distinct numbers at play here:
1) the maximum amount the "sugar lobby" is willing to pay to stop sugar laws being introduced - this is the amount you call $X, and is (as you say) equal to the total discounted profits that would be lost if a tax were introduced.
2) the amount the lobby actually pays. Assuming I read you correctly, this stands at $50m in 2009.
As you say, (1) is higher than (2), but not just because of externalities and uncertainties: there's also the fact that (1) is determined by total costs and benefits, and (2) by marginal costs and benefits in terms of how much additional lobbying money translates into reducing the probability of a tax being introduced (this is a generally important distinction, but I'll ignore it for now)
What we primarily care about is a third number, which is the minimum cost of buying out the sugar lobby. In a "certain" world (where lobbyists can knowingly guarantee a policy does or doesn't get passed by spending certain amounts) I think this corresponds the difference in these numbers, i.e. $(X-50m). That is, a philanthropist could go to the sugar lobby and say, we'll give you $(X-49.9999m), you the lobbyist save $50m that you would have spent on lobbying, and you lose $X in profits because of the tax. Therefore, you're made very slightly better off by this deal. Note that for a given X, the higher the spending on lobbying, the easier it is to pay off the lobbyist.
[In reality, the sugar lobby could play hardball and bargain up the buy-out price, hence minimum cost, but that's not really the point]
The point is we don't know what $X is - you'd probably need to look at total sugar consumption multiplied by proposed per unit tax minus the deadweight loss due to falling consumption. This in turn requires you to know the shape of the beverage industry's marginal cost curve.
I think you've conflated all three numbers at various points, having seen the lobby spends $50m, and then taken that as the cost to a philanthropist of getting a tax introduced.
I haven't checked the rest of your numbers, or thought about practical/political challenges, but I think the main stumbling block is the fact that it'll cost way more than $50m to buy out the sugar lobby.
The alternative that neither of us consider is the cost of counter-lobbying lawmakers to ignore the sugar lobby and introduce the tax - that's a whole different question and may well be cost-effective.
If I'm misrepresenting or misunderstanding what you're saying, I do apologise! I also wouldn't be surprised if a political economist spotted some errors in my analysis, but I'd still expect the $50m figure you quote to be misleading and a significant underestimate.