"You better cut the pizza in four pieces because I'm not hungry enough to eat six."From this perspective, a stock split makes the slices smaller, but there are more slices. Financial economists have studied why companies do stock splits at least since Fama, Fisher, Jensen, and Rolle's 1976 paper. FFJR found that increases in split-stock prices reversed if the splitting company didn't raise dividends in the period following the split.
The Motley Fool gets the story right in this piece titled "Buying Stock Around Splits":
Is it better to buy a company before or after it splits? That's like asking, 'Should I eat this peanut butter and jelly sandwich before or after mom cuts it in half?'"Of course, there are other reasons given why splits might increase shareholder wealth. One commonly cited reason is that by moving prices per share into a lower range, the company becomes more attractive to individual investors (as opposed to institutions). In a recent piece, Dhar, Goetzmann, and Zhu find that:
...The real reason to smile at a split announcement is because it signals that management is bullish. Companies are not likely to split their stock if they expect the price to go down.
A higher fraction of post-split trades are made by less sophisticated investors, as individual investors increase and professional investors reduce their aggregate buying activity following stock splits. This behavior supports the common practitioners' belief that stock splits help attract new investors and improve stock liquidity.