Gemara

(Beraisa): Whether or not there is an Ones, the first Bi'ah may not be on Motza'ei Shabbos.

(R. Zeira): This is lest he make calculations on Shabbos for the feast.

Objection (Abaye): On Shabbos, one may make calculations for a Mitzvah!

Rav Chisda and Rav Hamnuna said so explicitly.

(R. Elazar): We may apportion Tzedakah to the poor on Shabbos.

(R. Yakov): On Shabbos we go to Batei Kenesiyos and Batei Medrashos to oversee communal concerns.

(R. Yakov bar Idi): We oversee mortal issues on Shabbos.

(R. Shmuel bar Nachmani): On Shabbos we go to theaters and stadiums to oversee communal concerns.

(R. Menasiya): On Shabbos one may arrange Kidushin for his daughter and teachers to teach Torah or a trade to his son.

Shabbos 150a: "Mi'Mtzo Cheftzecha v'Daber Davar" - your desires are forbidden, but Shomayim's desires (Mitzvos) are permitted.

Rishonim

Rif and Rosh (Shabbos 64a and 23:4): "Cheftzecha" are forbidden, but speech about Shomayim's concerns, i.e. Mitzvos, are permitted. On Shabbos, one may make calculations for a Mitzvah, apportion Tzedakah go to Batei Kenesiyos and Batei Medrashos to oversee communal concerns, oversee mortal issues, go to theaters and stadiums to oversee communal concerns, and arrange Kidushin for his daughter and teachers for his son on Shabbos.

Hagahah (of R. Shmuel): Regarding the Heter to go to theaters and stadiums to oversee communal concerns, it should not say 'on Shabbos'. Even during the week one needs this Heter. If not, it is forbidden due to "Moshav Letzim" (the company of scoffers).

Rebuttal (Shiltei ha'Giborim 2): Here we discuss going to assembly rooms. The only Chidush is that it is permitted on Shabbos.

Rambam (Hilchos Shabbos 24:5): On Shabbos one may make calculations for a Mitzvah. We apportion Tzedakah, go to Batei Kenesiyos and Batei Medrashos to oversee communal concerns, and even to theaters and assembly rooms of Nochrim. One may arrange Kidushin for his daughter and teachers to teach his son Torah or a trade.

Magid Mishneh: We do not permit telling a Nochri to do Melachah or any Isur mid'Rabanan for the sake of communal concerns, except for the Heter to discuss them.

Poskim

Shulchan Aruch (OC 306:6): One may speak about concerns of Shomayim, e.g. calculations for a Mitzvah.

Magen Avraham (8): We may plan what is needed for a Seudas Mitzvah, like we find in Kesuvos (5a).

Shulchan Aruch (ibid.): We apportion Tzedakah

Question (Ran DH Poskin): Why may we apportion Tzedakah? One may not make Hekdesh! R. Chananel forbids to be Makdish a particular Keli, for this looks like business, but one may obligate himself to Hekdesh. This does not satisfy me, for one may not pledge Ploni's Erech (a fixed amount based on Ploni's age and gender), even though there is no Keli!

Answer (Beis Yosef DH v'Al): Vowing to give Ploni's Erech is like buying him. The Kolbo says that only Hekdesh to Bedek ha'Bayis or the Mizbe'ach is forbidden, for the item goes from his Reshus to Hekdesh. Nowadays our 'Hekdesh' is for the Sefer Torah, a crown, oil for lighting (the Beis ha'Keneses) and similar matters. This is permitted, for the item does not leave his Reshus. It is unlike business. This is like R. Chananel.

Magen Avraham (11): The Kolbo meant that our Hekdesh is really Chulin (CM 95). All of Yisrael have a share in it, including the Makdish. Therefore, it did not leave his Reshus.

Taz (2): According to the Beis Yosef, if one designated a Sefer Torah and brought it to the Beis ha'Keneses it is forbidden, for it changes Reshus. However, people do so! It seems that they are Makdish it privately before Shabbos, just they publicize it on Shabbos. One should not be Makdish something on Shabbos or bring it to the Beis ha'Keneses if he did not Makdish it before Shabbos.

Eshel Avraham (15): Hekdesh is forbidden because it is like business. If the only problem was "v'Daber Davar", it would be permitted. One may obligate himself to give to a Chasan who expounds on Shabbos, because it is not binding; one may retract.

Shulchan Aruch (ibid.): One may oversee communal concerns or arrange Kidushin for his son.

Mishnah Berurah (29): This should say 'for his daughter'.

Kaf ha'Chayim (50): One should not do a Kinyan Chalifin. Pesach ha'Devir permits a man who has not fulfilled Peru u'Rvu to mention an amount. His proofs are not decisive. The Beis Yosef forbids. Perhaps the custom is to rely on the lenient opinion. One should be careful if possible.

Shulchan Aruch (ibid.): One may arrange teachers to teach his son Torah or a trade. One may only ask if he wants to teach him. He may not hire him or mention a wage.

Hagahos Mordechai (Shabbos, Siman 459): If one asked a Nochri to do a Melachah and fixed the wage, we are not concerned if the Nochri does it on Shabbos, for this is his own volition. Therefore, one may fix a wage on Shabbos. When it is possible without this, we do not allow fixing a wage.

Beis Yosef (DH veha'Rav): The Mordechai permits fixing a wage when necessary. However, the Tur and Hagahos Maimoniyos (24:5) forbid this in the name of Maharam me'Rotenburg, and also the Ramban, Ran and Magid Mishneh forbid.

Rema: Some say that in places where they say 'Mi she'Berach' to one who gets an Aliyah and he pledges to Tzedakah or the Chazan, it is forbidden on Shabbos to say how much he will give. The custom is to be lenient, for it is permitted to apportion Tzedakah.

Magen Avraham (15): If the Chazan is rich, this is not Tzedakah! We must say that since we give to him to pray for the Tzibur, it is the needs of a Mitzvah, like money to build a Beis ha'Keneses.

Yam Shel Shlomo (Beitzah 5:8, brought in Magen Avraham 15): Auctioning off Mitzvos should be forbidden for it looks like business, unless we say that business does not apply to Mitzvos, only to items. This is a weak defense of the custom. Surely it is forbidden to buy places in the Beis ha'Keneses, or Esrogim after the Mitzvah is over. In Austria, pious people give to Tzedakah whatever they pledged, even if they did not receive the Mitzvah. This is like pledging Tzedakah. It is not like business at all. This permits even buying places and houses from Tzedakah. One who fears Shomayim should be careful about this.

Kaf ha'Chayim (42): Nowadays the custom is that only the one who gets the Mitzvah pays. Where places are lenient, they have on whom to rely.

Magen Avraham (15): Shiltei ha'Giborim is skeptical about buying Mitzvos. In Bava Kama he permits one who bought a Mitzvah to sell it to another.

Kaf ha'Chayim (43): One may say how much Tzedakah he pledges, even to a particular poor person. One may not do so when hiring a teacher. The teacher can demand the wage, so it is like business. Therefore, there is no problem if one who receives an Aliyah vows to give a certain amount to the Beis ha'Keneses or Chazan. I do not understand why anyone forbids.