Why does the Torah command us to collect a half of a shekel? After all, once a collection is being made, it would definitely be more logical (and profitable) to collect a whole shekel instead of half!
This special law that each member of Klal Yisrael must bring a Machatzit HaShekel (a half of a shekel) suggests that the very concept of a "machatzit" may be significant.
The standard (and I think correct) explanation is that by giving a 'fraction' of a value - as opposed to whole - the individual shows that he is an integral part of a more complete entity. Each individual Jew is not an entity by himself; rather he is a fraction or segment of Klal Yisrael.
Using a 'tree' parable, the nature of the relationship between the individual and the group can be understood in two ways:
Based on this understanding, we can advance a possible reason for giving a "machazit ha'shekel" when taking a census. Should we count each person individually, we focus on the independent nature of each individual. On the other hand, by counting the nation collectively, each person giving a "machazit ha'shekel," we focus of the collective nature of the nation. Considering that God has given Am Yisrael a Divine purpose as a collective group, i.e. to become God's special nation, then God may judge each individual more leniently in order that he can fulfill that Divine purpose.
Moreover, counting each person individually may reflect a lack of understanding of the collective nature of Am Yisrael, thus invoking God's anger (see 30:12 - "v'lo yihiyeh ba'hem negef b'fkod otam...").
[It is interesting to note that the money collected from "machazit ha'shekel" is used to buy the korbanot tzibur, the collective offering brought each day in the Temple.]
For Further Iyun
A. Read I Divrei Hayamim chapter 21. In that chapter, David HaMelech conducts an unnecessary census of Bnei Yisrael, which kindles God's anger. God gives David a choice of three punishments, from which David chooses the most severe one from the hand of God (what we say everyday in tachanun). After this plague has taken some 70,000 casualties, the plague stops when David offers a korban on the field of Arnan the Jebusite, which later becomes the site of the Mizbayach and the Bet HaMikdash on Har HaBayit.
Once again, we find a connection between the Mizbayach and Ohel Mo'ed (the Mikdash) and counting the nation.
See the various commentators on that chapter (and on the parallel chapter in Sefer Shmuel II chapter 24) concerning why it was improper for David to count the people.
See also Rashi on Shmot 30:11.
B. In Parshat Ki-Tisa, i.e. Parshat Shkalim (Shmot 30:11-16), it is not clear what specific type of census the psukim are referring to. The possibilities raised by the commentators include:
C. In our shiur on Yom Kippur, we suggested that kipur (or kappara) may imply 'protection' from a punishment that one may deserve. Relate this concept to Shmot 30:12, where the machazit hashekel is referred to as "kofer nafsho," and later as "kesef hakippurim."
Does this relate in away to the question above (B)?
Relate this to the concept of Dam HaKippurim found in relation to the Mizbach HaK'toret (see 30:7-10), and our shiur on Parshat Tezaveh.