Discounting of delayed food rewards in pigeons and rats: is there a magnitude effect?

Leonard and team tested pigeons and rats in a Skinner box. Birds pecked a disk. Rats pressed a lever.

Each choice gave food. One side paid one pellet right away. The other side paid two or four pellets after a delay.

Delays grew from 0 to 20 seconds across trials. The question: do bigger rewards make animals wait longer?

Both species followed the same hyperbolic curve. Value dropped fast at short delays, then slowed.

Surprise: doubling or quadrupling the food did not change the curve’s steepness. No “magnitude effect” appeared.

Gowen et al. (2013) later saw a magnitude effect in pigeons using a concurrent-chains setup. The birds switched from impulsive to self-control as added delays lengthened. The clash looks real, but the 2013 task let birds “sample” both options first—Leonard’s did not.

Nickerson et al. (2015) extended the rat work. They showed that daily exposure to delayed food made rats pick the large-later option more often. Leonard described choice; S showed you can change it.

Arroyo Antúnez et al. (2026) found bigger alternative rewards cause faster suppression and stronger resurgence in mice. Their “bigger reward, bigger impact” pattern differs from Leonard’s flat curve, but the paradigms—extinction vs. simple choice—are apples and oranges.

For your clients, reward size and delay both matter, but they may not multiply. If a kid picks 1 cookie now vs. 2 cookies after homework, doubling to 4 cookies might not help unless you also let them “see” the future payoff. Use visual timers, contracts, or token boards to bridge the gap. Test before you assume bigger is better.