The funny thing about keeping score in your relationship is this: No one actually wins.
Keeping track of who does what for whom (a "tit-for-tat" game) is a sign you are not seeing your behaviors as benefiting the relationship, but just as benefiting one partner or the other. Try to see how your actions benefit the relationship, because, ultimately, your relationship ultimately benefits you both.
Harman's words echo results of recent research on happy marriages, suggesting that it's better to believe that you're both on the same team. And if that's true, then there's no point in keeping score.