One of the more nuanced critiques of the literature on human cognitive biases is that some of them posit conflicting effects. Probably the most glaring discrepancy is the difference between the primacy and the recency effect in hypothesis formation. Which factor is more important? Marsh and Ahn take on the challenge in their 2006 paper,
Some studies have shown a recency effect: Information that is presented later in a sequence is more heavily reflected in judgments than is information that is presented earlier. Other studies have shown a primacy effect: Early-presented information is reflected in judgment more than is later information…
Throughout this study, we have maintained the position that the primacy effect is obtained because people form a hypothesis from earlier data and underadjust this hypothesis… The primacy effect was found to be moderated by the cognitive load required by the hypothesis-testing nature of the task and by the size of the verbal working memory capacity available to process information.
Unless the subject is overloaded with information, the primacy effect is dominant. A real world application can be found in the work of Trevon Logan, who analyzed college football votes in order to see which games had more of an impact on the rankings of AP voters. Consistent with the idea that primacy is more salient than recency, he found that it is better to lose later in the season than earlier.
In order to be rational, you must obfuscate your initial opinions and see the whole story before you begin to draw conclusions. If you must choose, err on the side of weighing the later data more heavily in order to compensate for your cognitive flaws.
Marsh JK, Ahn, W. 2006 Order effects in contingency learning: The role of task complexity. Memory & Cognition 34:568-576. Abstract.