One can devise a Poison Pill in such a way that it reduces the effectiveness of a hostile takeover by allowing existing shareholders (But not the acquirer) to purchase shares at a discount. This means that having bought a certain percentage of Yahoo! (in this case, 15%), Yahoo! shareholders can then get more shares at a huge discount. This means that the percentage of shares owned by Microsoft will come be less than 15% and may not be enough for a takeover. This is called a Dilution Poison Pill.
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You missed a couple key features of this type of poison pill, sometimes called a “flip-in” shareholder rights plan. It is a very common (in not the most common) type of takeover prevention mechanism. I don’t know the particular details of Yahoo!’s rights plan, but here is an illustration of how such a plan is indeed effective because it poses a credible threat.

In short, a “dilution poison pill” as you called it, doesn’t really harm anybody except the entity attempting to acquire the company:

The “pill” become triggered when a single entity (Acquiring Person) comes into possession of more than a certain percentage of stock (we’ll assume 10% here) without the Target Company’s approval. When this occurs, each share of stock, except for those belonging to the Acquiring Person, is entitled to buy another share of stock at a substantially discounted price (say 50% of the current market price). A share of the stock should reflect its proportionate share of the value of the company. Assume that Company Y is worth $100 and has 10 outstanding shares (each worth $10). and that Company Z has acquired 10% of the stock (1 share):

Y chooses to oppose the takeover by allowing the public shareholders to exercise their right to buy the discounted shares from the company treasury:

Y sells 9 new shares at $5 each, netting $45 for the company. The company is now worth $145 ($100 initial value + cash proceeds from stock sale) and has 19 outstanding shares (18 at-large, 1 owned by Z).

Each share is now worth $145/19=$7.63. What was the net result of “swallowing the pill” to the shareholders at-large (those other than Z)?: Each now has two shares of Y’s stock, and thus has an investment valued at $15.26. This represents a net gain of $0.26 for each shareholder ($10 initial value of share plus $5 cost of discounted share).

Z still owns only 1 share of Y stock, and thus suffered a loss of $2.37 (a 23.7% drop!).

And there we are–the threat is credible. This takeover defense essentially just redistributes value from the Acquiring Person to the other shareholders of the company.

You wrote:

Will this be effective? Let’s say that microsoft has bought 15% of Yahoo! stock for tens of billions of dollars. That money is a sunk cost. Once they’re bought, they’re bought. Microsoft must treat this as a sunk cost, and continue to buy up more Yahoo! shares to gain a controlling interest since the additional cost of buying the shares is much less than the amount already sunk in. So this Poison Pill holds no threat either.
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The shares aren’t a sunk cost for Microsoft–they have an intrinsic value and can be sold on the market.