Gemarah Bava Metzia (49a) איתמר דברים רב אמר אין בהן משום מחוסרי אמנה ורבי יוחנן אמר ביש בהם משום מחוסרי אמנה מיתיבי רבי יוסי ברבי יהודה אומר מה תלמוד לומר (ויקרא יט, לו) הין צדק והלא הין בכלל איפה היה אלא לומר לך שיהא הן שלך צדק ולאו שלך צדק אמר אביי ההוא דשלא ידבר אחד בפה ואחד בלב. Rashi says שלא ידבר אחד בפה כו' - בשעה שהוא אומר הדבור לא יהא בדעתו לשנות אבל אם נשתנה השער לאחר זמן והוא חוזר בו לפי שינוי השער אין כאן חסרון אמנה.
The Rosh (siman 12) asks why does the Rif cite the law of שלא ידבר אחד בפה ואחד בלב if we rule like Rav Yochanan that there is מחוסר אמנה on retracting from one's words, then that is the derash leaned out from the possuk? The Rosh answers since the Gemarah later on the page qualifies the statement of Rav Yochanan that there is מחוסר אמנה for words only if it is a promise to give a small present, then the source for R. Y. can't be the possuk for if so there would be no such difference, rather R.Y.'s din must be an independent sevarah and indeed the possuk teaches us שלא ידבר אחד בפה ואחד בלב. What is the difference between if the law is derived from a possuk or a sevarah?
Why is it considered in bad faith to recant only from a small present? Rashi explains משום דסמכא דעתיה דמקבל אדיבוריה וכי אמר מותר לחזור בו במתנה מרובה קאמר דלא סמכא דעתיה דמקבל דלקיימיה לדיבוריה. If it a small present the receipt assumes the one making the promise will keep his word but if it is something large, he knows that there is a great possibility he will renege.
We can have a chakirah what is this halacha of מחוסר אמנה, "bad faith," is it a din in the giver, the גברא making the promise, not to be a liar (like a middos din,) or is it a din for the sake of the recipient, not to violate his trust.
The Rosh understood if the law of מחוסר אמנה was based upon the possuk, it is a din in הן צדק, for one to keep their word, not to be a liar, and it doesn't matter what the recipient thinks ,either way the one that made the promise must keep his word. If we see the Gemarah is saying that מחוסר אמנה depends on if the recipient feels violated, then it must be his halacha is not derived from the possuk and he needs the possuk to be telling us שלא ידבר אחד בפה ואחד בלב as well.
With this idea we can explain Rashi as well. Rashi says in the answer of the Gemarah שלא ידבר אחד בפה ואחד בלב that Rav agrees you can't make a promise with intent to break it but if the market value changes, אבל אם נשתנה השער לאחר זמן והוא חוזר בו לפי שינוי השער, then there is no issue of חסרון אמנה. Why does Rashi have to introduce the market value changing, just say if you didn't intentionally lie, there is no issue of חסרון אמנה? We see Rashi holds the machlokes Rav and R.Y. is if the promisor must be totally truthful, however everyone agrees there is a concept of מחוסר אמנה if one is just violates the trust of the recipient for no reason at all.
Tosfos Bava Bathra (123b) says בכל דוכתא עביד מכירי כהונה מוחזק בפרק כל הגט (גיטין דף ל.) המלוה מעות את הכהן והלוי והיינו טעמא שזהו מתנה מועטת ואסור לחזור בו ואפי' בדברי' בעלמא ואע"פ שאם רצה יכול לחזור בו מכל מקום כל כמה דלא הדר הוי כמוחזק. Tosfos holds due to the law of מחוסר אמנה the kohan is considered muchzak in priestly presents normally given to him. We see from Tosfos that מחוסר אמנה is obviously a din reflective of the recipient but Tosfos goes a step further and says that the present is viewed as muchzak (so that a bechor can receive double portion from it,) in the hands of the recipient. Rav Shmuel Rozovsky says we see Tosfos must hold that מחוסר אמנה mean not only can the recipient grumble if he doesn't receive what is promised to him, but he is considered to have a monetary rights to the promised object.
The Rosh in Teshuvot (102:10) says if one promised the rights to be the מוהל of his son to an individual and then decides to give it to someone else, there is no problem of מחוסר אמנה because that only applies to something that a kinyan can take affect on but the rights to do the milah which there is no way to make a binding kinyan on, there is no violation of מחוסר אמנה when backing out. This only makes sense if the issue of מחוסר אמנה is violating the recipient, if the law is to be stand up guy, it should not depend upon the laws of kinyanim. Why would מחוסר אמנה apply only when a kinyan does? It would seem the Rosh holds the law of מחוסר אמנה is an extension of the law of kinyan to one's words, one's words creating a kinyan bind vis-a-vis the law of מחוסר אמנה. In light of the Tosfos in Bava Bathra it is clearer that the law of מחוסר אמנה has to create a monetary right for the recipient and that can only exist on something that has a kinyan (based upon a shir by R' Elefant.)
The Rambam (Mechirah 7:9) says וְכֵן מִי שֶׁאָמַר לַחֲבֵרוֹ לִתֵּן לוֹ מַתָּנָה וְלֹא נָתַן הֲרֵי זֶה מִמְּחֻסְּרֵי אֲמָנָה. בַּמֶּה דְּבָרִים אֲמוּרִים בְּמַתָּנָה מוּעֶטֶת שֶׁהֲרֵי סָמְכָה דַּעְתּוֹ שֶׁל מְקַבֵּל כְּשֶׁהִבְטִיחוֹ. אֲבָל בְּמַתָּנָה מְרֻבָּה אֵין בָּהּ חֶסְרוֹן אֲמָנָה. שֶׁהֲרֵי לֹא הֶאֱמִין זֶה שֶׁיִּתֵּן לוֹ דְּבָרִים אֵלּוּ עַד שֶׁיִּקְנֶה אוֹתָן בִּדְבָרִים שֶׁקּוֹנִין בָּהֶן. This is the din of Rav Yochanan. The Rambam (Deot 5:13) says מַשָּׂאוֹ וּמַתָּנוֹ שֶׁל תַּלְמִיד חָכָם בֶּאֱמֶת וּבֶאֱמוּנָה. אוֹמֵר עַל לָאו לָאו וְעַל הֵן הֵן. This line would seem to come from the Gemarah שיהא הן שלך צדק ולאו שלך צדק. It is noteworthy that this is cited in Hilchot Deot indicating it is just a measure of good behavior, not a din in Mechirah like the law of מחוסר אמנה. However, the Rambam doesn't cite the law שלא ידבר אחד בפה ואחד בלב like the Rif, he cites the simple read of the berasah שיהא הן שלך צדק ולאו שלך צדק. It sounds like the Rambam also holds that there are two tiers. One law is that of R.Y. which is a kinyan law, a law to not disappoint the recipient. The possuk tells us שיהא הן שלך צדק ולאו שלך צדק (presumably the Rambam would have to say like the Rosh that R.Y.'s din doesn't emanate from the the possuk but then we are free to say the possuk is telling us another law, to be a standup individual and always keep one's word. Also, it is clear the Rambam says this in the context of a talmud chacham, it seems this additional enhancement of always keeping one's word in only necessary for a talmud chacham, וצ"ע. However, in Deot (2:6) the Rambam says אָסוּר לָאָדָם לְהַנְהִיג עַצְמוֹ בְּדִבְרֵי חֲלָקוֹת וּפִתּוּי. וְלֹא יִהְיֶה אֶחָד בַּפֶּה וְאֶחָד בַּלֵּב אֶלָּא תּוֹכוֹ כְּבָרוֹ וְהָעִנְיָן שֶׁבַּלֵּב הוּא הַדָּבָר שֶׁבַּפֶּה. Here he does say וְלֹא יִהְיֶה אֶחָד בַּפֶּה וְאֶחָד like the Gemarah says and he records it as a mode of behavior for everyone. This would follow the Rif of the second tier of the right way to act is וְלֹא יִהְיֶה אֶחָד בַּפֶּה וְאֶחָד בַּלֵּב, but how does the Rambam know three levels, the level of מחוסר אמנה, a kinyan law, applies only as to not upset the recipient and then two distinct levels of proper behavior, one for everyone וְלֹא יִהְיֶה אֶחָד בַּפֶּה וְאֶחָד בַּלֵּב and another level for a talmud chacham to always keep their word, וצ"ע.