While considering where to look for evidence that Israel is deterred by Hamas, I thought of something that seems totally obvious once it is said: If the reward I offer you for not attacking me is worse than my attacks against you if you do, you will keep attacking me. In other words: Deterrence is not only about threats of punishment, it is also about rewarding "good" behavior. In order for Israel to decide not to attack Hamas in the Gaza Strip, Hamas has to offer something more enticing to Israel in return. If its alternative is "dissolve yourself," Israel is obviously not going to choose to be deterred.
Again, this may seem obvious, but it is an interesting nuance because most people associate policies of deterrence with so-called foreign policy hawks. This is because the main feature of the type of deterrence that has dominated world politics for decades is threats of unacceptable retaliation for attacks (think of the US and Soviet policy of Mutually Assured Destruction when it came to nuclear attacks). Deterrence is certainly not a cuddly, "let's let in the Age of Aquarius" sort of foreign policy stance. But the alternative to attacking the US in the case above was peace, since deterrence was mutual. Peace is a pretty nice alternative to nuclear war, so it stuck. Crucially, destroying the Soviet Union was not a US policy (though many in the US openly wished for it).
The case with the US also illustrates another factor: Further alternatives must be less palatable than accepting deterrence. The main alternative was wiping the US out before it could strike back, thus removing the threat and the constraint of US deterrence on Soviet policymaking. This policy was unrealistic, and the US explicitly made sure of this by ensuring that the Soviet Union could never be certain of wiping out the whole US nuclear arsenal, meaning its own destruction would likely be imminent if it attacked the US. No realistic alternative there.
The main things required to block the alternative route of wiping out an enemy are power and resilience (two things the US nuclear arsenal had and has in abundance). In light of this, Hamas's strengthening in recent years may actually be a blessing in disguise for peace in the Middle East, if not necessarily for Israel's ambitions. Hamas has shown that, with occupation or without it, Israel cannot eliminate the organization without taking measures that it would not consider (like wiping out the entire Gaza Strip). For a while in the early to mid-2000s, with Israeli security stopping the vast majority of suicide bombings by 2005, it looked like Israel might be able to defeat Hamas militarily and thus need not be bound by any Hamas attempts to deter it. Rocket attacks have changed this prospect. Bombers could be stopped from entering Israel, rockets cannot. Even the Iron Dome missile defense system could not stop a concerted effort: A massive number of rockets flying toward Israel would overwhelm the system.
It therefore seems that Israel would be extremely hard-pressed to either eliminate Hamas or deny it the ability to attack Israel. This means that the choice of accepting a sort of truce with Hamas has become more palatable.
Going back to the main point of this post, the "peaceful" alternative has also become more available from Hamas's side as it has moderated its actions (if not much of its rhetoric) over the years to allow for short- to medium-terms cease-fires with Israel. In other words, Hamas needed to become more dovish to stop Israeli attacks.
Will this be a permanent change? Anyone who tries to predict the future in the Middle East is a fool. Hamas's continued grip on the Gaza Strip is not assured, and there are other, less moderate groups, who are too Hawkish to deter Israel. Dovishness on the part of Hamas has also been encouraged by Israel's massive superiority. This differential, too, is not written in stone. Over time, things could change and destabilize the current situation. Finally, since this set-up is based on both sides' perceptions of their and their opponent's power and the credibility of their threats, a change simply in the perception of the situation could spark another round of violence. My guess would be that such a round would eventually return to a tenuous peace, but how peaceful is a situation that repeatedly erupts into violence every few years?
For these reasons, the future is dependent on whether or not Israel and Hamas take further steps towards cementing peace. Everyone knows this, so there is no need to discuss it. My hypothesis, however, is that deterrence may help give the two parties the breathing room they need to move forward--if they are bold enough.
