Since a Chinese syllable can correspond to many characters (homophones), the syllable-to-character conversion task is quite challenging for Chinese phonetic input methods (CPIM). There are usually two stages in a CPIM: 1. segment the syllable sequence into syllable words, and 2. select the most likely character words for each syllable word. A CPIM usually assumes that the input is a complete sentence, and evaluates the performance based on a well-formed corpus. However, in practice, most Pinyin users prefer progressive text entry in several short chunks, mainly in one or two words each (most Chinese words consist of two or more characters). Short chunks do not provide enough contexts to perform the best possible syllable-to-character conversion, especially when a chunk consists of overlapping syllable words. In such cases, a conversion system often selects the boundary of a word with the highest frequency. Short chunk input is even more popular on platforms with limited computing power, such as mobile phones. Based on the observation that the relative strength of a word can be quite different when calculated leftwards or rightwards, we propose a simple division of the word context into the left context and the right context. Furthermore, we design a double ranking strategy for each word to reduce the number of errors in Step 1. Our strategy is modeled as the minimum feedback arc set problem on bipartite tournament with approximate solutions derived from genetic algorithm. Experiments show that, compared to the frequency-based method (FBM) (low memory and fast) and the conditional random fields (CRF) model (larger memory and slower), our double ranking strategy has the benefits of less memory and low power requirement with competitive performance. We believe a similar strategy could also be adopted to disambiguate conflicting linguistic patterns effectively.