Rationality is the logical progress toward a chosen goal. Whether a decision is rational or not is entirely dependent upon the goal being sought. The logic is there merely to serve the goal, “chosen purpose”.
What you are calling “emotions” are actually subconscious rationalities, each with its own goal. Emotional dissonance occurs when there is disharmony between the inner, subconscious willingness to hold off one goal for sake of another. It is an exact analogy to the House of Representatives voting on individual issues (goals). In the case of the House, the “logic” involved is simply a voting procedure, an attempt to balance public pressure disregarding higher strategies. It represents an urge being put forth by the populous and is often quite irrational toward higher national strategies and truer needs.
The purpose of the Senate is to balance the populous urging (the “emotions”) into a more rational strategy that includes more fixed concerns of which the House is often unaware. The Senate is more of the “thinker” involved and less of the emotive, more logic oriented and less passion oriented.
The conscious mind is in effect that Senate having to try to balance the passions stemming from the House into a single direction of action so that the nation can act as a whole and still manage to accomplish as much of the passion based concerns as possible, if possible.
The President is supposed to do nothing more than militarily carry out the laws presented to him while adding the consideration of military issues of which the Senate might not be immediately aware. Of course in reality these days, none of it really works quite that way any more as outer influences corrupt the system.
That exact same process is what causes an individual to be irrational as well as the society as a whole.
Loss of strategy or the corruption of it by passions (choices) being exercised in the wrong order or by the wrong governing authority (such as the President deciding to maintain a war for sake of obtaining continuous power) destroys otherwise rational strategies. What was proposed as a logical means to obtain a reasonable goal gets lost because the strategy isn’t being carried out.
Dictators, socialists, and communists all attempt to be rid of the “dissonant” because emotive dissonance is the issue. The problem is, “issue for whom?” For which goal? Who actually chose the goal? The dictatorial systems dictate the only goals. The democratic systems surmise the goal from sensing the urgings, the “emotions” and balancing them. Democracy requires more forethought, time, and care. Dictatorial systems adopt a defined “good” and strategize toward it by their own presumptions.
So in the long run, one cannot say that a society is “irrational” without presuming what the goal of the society actually is. Invariably, the people will be told that the goal is one thing while in reality the governing authority (often not even a citizen of that country) maintains an entirely different goal. So from the stance of the people, the society very often appears irrational because they are not privy to the leaders goals. At times, the leaders see it as irrational because they are not getting their goals and presume theirs are the only important goals, “people do not have the sense to govern themselves”.
Emotionalism within the individuals merely makes it easier for the dictator to ensure his authority over them, keeping them weak. And then because they propose irrational urgings, the higher authority has greater impetus for ignoring them.
The true irrationality comes in when the simple minded (as vast as it might be) strategies of the dictator do not truly compensate for the real situation of the populous and the nation as a whole suffers. This issue gets hidden by replacing the loss of life from one generation by the next, an effort to grow faster than ones foolishness is killing him.
So it isn’t really an issue of logic versus emotion. It is an issue of choosing the goals. The logic and strategies are easy enough. Even computers and Science can handle those kinds of things. The key to all rationality is simply choosing the goal, the “emotive” behind the strategy. Scramble the emotions, creating dissonance within, and there is no consensus of goal and thus irrationality ensues and no logic can serve for no one is really following any particular plan.
One cannot make a rational decision if he hasn’t decided to where he is headed.